This opener has been tested purely at Deity on Pangea maps. It will not work nearly as well on lower difficulties since I imagine that you'll struggle to find suitable trading partners early on in the game. The basic jist of the strategy is to abuse Shoshone's ability to generate ludicrous sums of gold early on by fully exploiting the resources from their land in addition to abusing their control over their ancient ruins to create a tall, scientific powerhouse.
To give you an idea, look at this. Yes, this is Deity. Sub 220 wins are possible with this strategy.
Rough Capitol BO:
Pathfinder -> Pathfinder (skip if you have mining luxury resources not covered with jungles OR 3+ forests to chop) -> Worker -> Shrine (skip if you find a faith ruin past turn 20) -> Settler -> Settler -> Settler (if not rush bought) -> Granary -> Library -> Oracle if you have heavy production and can finish it by turn ~80 (skip otherwise) -> Caravan (skip if you get Oracle, build in your first expansion instead) -> National College -> Writer's Guild -> University (as it becomes available) -> Market -> Caravansary -> Artists's Guild -> Porcelain Tower (finish by the time the first World Congress vote happens)
Shoshone, unlike most civs, can frequently find themselves looking at starts such as this. You get a lot of early land and plenty of access to 2 production tiles. When paired with their ability to grab an early population ruin or two it makes sense to open with a Tradition-focused build and churn out some early Settlers. Your ruin control will allow you nab a quick Legalism anyways (i.e. Monument isn't needed) and if you find a ruin past turn 20 then your pantheon will be secured as well (i.e. Shrine isn't always essential). Focusing on Pathfinders, Workers and Settlers just plain makes a lot of sense. I mean, why wait when you can just do this?
Whenever possible rush buy things like Water Mill, Workshop, Stone Works, Lighthouse, etc. They're cheap and essential but your Cap has so much to build and so little time to pump everything out. You need your gold buildings up asap to power your economy and you need your Guilds online to flesh out your culture needs.
For what it's worth I've never found a good time to build the Amphitheater and so I basically never do. It's too expensive + useless to buy and it requires too many hammers to build.
First expansion:
Granary -> Library -> Caravan (assuming that you're building Oracle in your Cap) -> Walls*
Second and third expansion:
Library -> Granary -> Walls*
*Walls should only be built if you're forward settling on an aggressive opponent such as the Zulus, Assyria, Aztecs, Rome, etc. You may need to go Library -> Walls in your forward cities if you're expanding into fearsome opponents and won't have much production early on (i.e. no time to go Library -> Granary -> Walls by turn ~80).
Key purchases:
Settler;
Worker;
Worker;
Library in your 4th city if required;
You want a ton of Workers when you're Shoshone. Having 6-7 rolling is highly desirable and you're the one civ who doesn't need to buy tiles (very often) and who usually has a ton of sellables that they can improve immediately. I always steal one, make one and you can often nab one from a Barb camp. The rest you'll probably have to buy but that's not a big deal usually.
Social Policy Progression:
Tradition Opener - Legalism - Monarchy - Landed Elite (you should obviously go LE first if you're planning to grow for a bit)
Patronage Opener - Consulates (this assumes that you got Oracle or some form of extra culture generation)
Aristocracy - Oligarchy (note that it's not always possible to open Patronage before getting Aristocracy, that's fine though)
Rationalism Opener - Secularism - Humanism - Free Thought
Order -> Young Pioneers + Social Realism - Worker's Facilities - Skyscrapers - Five-Year Plan
(Hero of the People isn't bad either and you can always grab more happiness policies as needed)
Finish Rationalism before your last batch of RAs finishes. You can usually finish the tree off shortly after you grab Worker's Facilities. This is especially true if you win the World's Fair and pop a Great Artist to get a Golden Age at the same time as you get the bonus culture. Pop all of your Great Writers 8 turns later for roughly 1500 culture each. You may have used one earlier to get Secularism faster but that's fine. You should have at least 2 to blow which is 2 full policies at this stage of the game.
This build basically assumes that you get Oracle which is quite reasonable on Deity insofar as you have a moderate amount of production. Anything other than pure grassland/floodplains/jungle should do the trick really. You can start it somewhere around turn 60 and finish it somewhere around turn 80. That's going to be good enough a huge % of the time. If you don't get Oracle just hop straight into Rationalism once Tradition finishes (unless you're getting a bunch of bonus culture from CSes or a Pantheon).
Priority Productions (roughly in order):
Tech - Workers as needed - Caravan(s) - Water Mill - Stone Works - Lighthouse - Amphitheater - Market - Caravansary (trade hubs only) Garden - Shrine - Circus - Workshop - Colosseum - Temple
Buildings such as Universities, Observatories, Public Schools, Factories (assuming Order) and Research Labs should be prioritized above everything else. Beyond that you want to focus on happiness, growth, great person generation, gold and production. Culture gets the raw end of the deal and won't get much love if you're not actively pursuing a CV. You definitely can't ignore it though. My basic culture acquisition strategy is to grab quick Amphitheaters in my expansions (I rarely build it in my Cap) and use those + Consulates + Guilds + winning the World's Fair to cover my needs. I basically never build Opera Houses or above in my cities.
Tech Path:
Pottery -> Mining (get this first if you have at least 1 mining luxury or 3+ forests to chop) -> Animal Husbandry -> Bronze Working/Masonry/Trapping if required -> Calendar -> Writing -> Philosophy* -> Bronze Working + any missing luxury techs -> Civil Service -> Sailing** -> Theology -> Education -> Construction*** -> Astronomy (if you have multiple cities and/or your Cap next to (a) mountain(s))-> Engineering -> Guilds -> Acoustics****.
*This should be done by turn ~60. That often means ignoring a luxury tech such as Masonry or Trapping. That's fine. You need to get a fast Philosophy for a fast Oracle. Between Calendar and either Bronze Working, Trapping or Masonry you be fine with happiness until turn ~75.
**Sailing shouldn't take more than 1-2 turns. Put it off until you have your NC + enough Libraries to pump it out without significantly hindering your sprint to Education. You're doing it wrong if it's taking you like 6 turns to churn it out.
***Pick this up as needed for happiness. You can go some games without ever building Colosseums so if you have plenty of luxuries just ignore the tech until you're forced to take it.
****Obviously you can beeline Acoustics after Education for social policy reasons if needed. Being able to open the Rationalism tree straight out of Tradition is a huge benefit if you're not going Consulates. So yeah, always try and make this happen if it's a possibility. No need to rush into the Renaissance otherwise.
This is basically your best bet regardless of the victory condition (VC) that you're pursuing. This strategy involves getting 4 very tall cities very quickly and amassing a ton of GPT to support them. From there you can win however you want. Bronze Working is worth grabbing early since you'll almost always have Iron and it's worth grabbing it to sell for 45g per. Engineering is useful for the extra Trade Route and Guilds is nice for getting your next Guild up and running. Ignore Archery whenever possible and simply use an upgrade ruin to grab an early Composite Bowman instead. It'll save you beakers and hammers.
Rough Ruin Priority:
The first faith > population > the first culture > unit upgrades > tech > gold.
The first ruin that you find is best used on population. You can only select the same option every 3 picks and since we want at least 2 of these it's important to get it first. Grab culture next to open Tradition up. Never take another culture ruin though. Grab an upgrade ruin next to get an early Composite Bowman. Next you'll want a second population and you can grab tech and gold as needed from there (tech > gold). The first ruin that you find past turn 19 is best used on faith to snag a quick and easy pantheon. Again, since you can't just chain the same option over and over you'll have to make due with tech and gold ruins as needed. Culture becomes rather worthless after the first so that stops being a realistic option in my mind. An ideal sequence would look something like: population (on turn 2) - culture - unit upgrade - population - tech - faith or something roughly along those lines. Finding 6ish ruins isn't difficult at all on Pangea maps against computers for what it's worth. Obviously if you only find 2 then you only find 2 and that's life.
Pathfinders upgrade to Composite Bows which are fantastic at clearing Barb camps for early city state (CS) quests and for staving early aggression off. I'm never unhappy to take 1 upgrade early on. It's usually enough to forgo Archery altogether in my experience since Comp Bows tend to ~3 shot most Barb Camps early on. Still, I'm not opposed to getting additional Comp Bows if possible either. They're incredibly useful during the scariest stages of the game.
Ruin Tactics:
Starting on turn 20 you can select 20 faith as a option for your ruins and so if you find one on turn 16 or later you're usually better off sitting and waiting for turn 20. This is completely safe if there's a nearby hill to provide vision but obviously it's risky if you're surrounded by jungle and can't see incoming scouts. At that point you have to make a judgment call. In the dark I'd opt to grab it and hope to find another but I mean it's your game. Population ruins should be given a similar treatment. If I'm growing in like a turn then I like to sit near a ruin and wait to grow before nabbing it. This is a fantastic way to spring straight to 5 pop to start churning Settlers out. Working 5x 2 production (hills, horses, most mining-based luxuries) produces a Settler extremely quickly (~7 turns) and given your massive starting land it's not unreasonable to have 5 workable ones right off the bat.
The Opening Turns:
The basic BO is to get 4 cities up and running with Libraries and Granaries so that you can rush out a National College around turn 100 so that you can start to grow big and strong. Steal a worker and improve everything that you can sell. Use that gold to buy workers, Libraries and defenses as needed.
Pathfinders are good versions of scouts/warriors but they take a long time to build. Still, you really need to get them out early on so that you abuse their ability to pick and choose your early game ruin benefits. I strongly recommend pumping out at least 1 because Shoshone typically doesn't need a super early Shrine to get a pantheon nor do they need a Monument to get early culture. You'll (virtually) always get a Pantheon and you'll (virtually) never have to wait very long for Legalism.
The first thing that we need to do is find ourselves a worker. Start by sending your Pathfinder (PF) exploring in a straight-ish line. Whenever possible walk over and/or end your turns on hills to maximize your sight. Don't worry about doubling back to check over your entire starting area; just keep trucking along looking for City States (CS)es and civs. When you meet your first civ you should strongly consider stealing a worker from him or her if they're within ~10 tiles of your Cap. Remember that your PFs are quite beefy compared to Scouts. They can take a shot or two from a city and still walk away with half of their HP. You can't eat 2 city shots + 2 warrior attacks but you can steal pretty much any relatively undefended worker and run away. A good rule of thumb is that you can survive "any 3 hits." Warrior hit + Archer hit + city hit, city hit + 2x Warrior hit, 3x Warrior hit, etc. will not kill a PF. Obviously stealing from a CS is easy since you can immediately make peace with them. The negative diplomacy modifier associated with starting an early war will quickly fade as well so there's basically no reason not to do it as long as you don't start more than one. Stealing a worker is one of the best and easiest ways to get ahead in the game.
Eventually you'll have 3 PFs running around looking for ruins, NWs, trading partners and CSes. If you find a religious civ early on then you can definitely skip the Shrine since 24-28 faith on turn ~20 is typically more than enough to secure a pantheon. Since you should have a worker by now you're basically just looking for NWs, all the civs and as many CSes as you can possible meet. Deity AIs get writing exceptionally fast so sell your embassy to each of them for 1gpt. That 210g will come in handy in a bit.
It's time to start pumping out a few Settlers. Lucky for us Shoshone gets fast + free population and usually has a few mines/2 hammer tiles to work. You'll hit 4-5 pop faster than any other civ and once you get there you can usually pop out 2 Settlers in 14-16 turns. That's pretty close to what Liberty manages. The last one can be built or bought depending on your gold situation. Just buy multiple workers instead if you decide to hard build all 3.
Once you have a worker or two back at home focus your efforts on improving everything that you can sell. This includes horses, iron, luxuries, anything. Horses and iron can be sold for 1gpt/per. Luxuries net you 6gpt. Ideally someone will offer you a declaration of friendship (DoF) at which point you can start selling things for lump sums of gold. Horses and iron are good for 45g/per and luxuries can get you 240g. Shoshone get a lot of land and what this means is that you'll usually have a lot to sell. Get it all improved asap and start generating some gold to buy a Settler and some Workers. Use those workers to improve more tiles and sell more luxuries and strategics. Abuse the fact that you get all of your resources in your opening borders at no cost. Whereas everyone else has to buy their way to luxuries you get them all automatically.
Disclaimer: Obviously you can get unlucky and be looking at bare land with nothing to sell. Shoshone isn't immune to that type of bad luck. My point is simply that they have a high probability of having immediate access to the vast majority of their resources. Whereas most civs need to buy tiles early on you can afford to spend that gold on other things.
Farming Workers:
Since this seems to confuse a lot of people, I'll briefly discuss farming Workers from AIs. When you find your first AI you'll want to look for one of their cities that still has unimproved tiles. Wait for a Worker to come by who can't be reached by many combat units in 1 turn. Grab it and quickly run 2 tiles away and heal. Pillage the tile if it was improved to ensure that more Workers will come back. A few turns later another Worker should come. After stealing 2 you can offer peace to the AI or more likely they'll offer peace to you. Just take it. 2 Workers is good enough. Sample:
I see a Worker. I see that the Warrior can't get to it in one turn.
I take Worker + Pillage tile to ensure that another Worker will come back for it.
Like moths to the flame...
All for Tich!
Barbarians:
This is an issue that arises often so I should probably address it. There's no one right way to handle Barbs in BnW. Sometimes you have plenty of nearby AIs who'll take care of any and all Barb camps for you. It's pointless to rush Archery in those spots. The only time Barbs give you fits (in my experience) are when you're isolated and when you randomly have 3 or more camps spawn nearby you. They'll still pester CSes and such a good % of the time but you can, on occasion, get absurdly unlucky and have them basically rally units at you even if there are other nearby civs/CSes. If you need Archery, take it. That's all that I can say really. It pops after a few turns and Archers are quick and easy to train/buy as needed. I realize that this isn't especially helpful, but really, I'm not sure what more people expect to hear. You'll have tons of scouting information from 3 Pathfinders so you yourself are going to have to make judgment calls about the Barbarian scum. I rarely find myself needing it since Deity AI stomp all over barb camps but if I'm isolated and surrounded by them then I'll obviously adapt.
It's also worth noting that Pathfinders upgrade to Composite Bows if you get a ruin upgrade. If you play one of those games where you find like 6+ ruins then feel free to grab a second Comp Bow (always get one with your third ruin). Use it to clear Barb Camps for CS quests, defend your Settlers, stave early aggression off, etc. You'll basically never need Archery as Shoshone.
City Placements:
Whenever possible expand on hills that have a mountain tile in their 1-ring radius, that have access to fresh water (i.e. a river) and that have a luxury anywhere in their 3-ring radius. That's obviously the "ideal scenario" but I mean that's what you should be looking for at all times. Having access to production and such is nice but I mean beggars can't afford to be choosers. Try to space your cities 6-8 tiles apart and do your best to avoid having an "outlier." Deity AIs LOVE to spam cities and it will be surrounded in no time and that will tick a lot of people off. Whenever you are lucky enough to have rivers nearby try and expand on them in such a way that computers will be forced to cross it in order to attack you. The river penalty combined with your hill bonus make taking your early cities extremely difficult. Take a look at this and see how it quickly became this a few turns later. No walls, no comp bows, just 2 archers and cities on hills behind rivers. Again, ideal scenario, sure, but it's still worth keeping in mind. Finally, remember that Shoshone can really abuse the 3 tile radius. Even though you won't get every luxury every time you'll still get most of them and the ones that you don't get should only be one quick tile purchase away. Normally you have to buy 2 tiles (~150 gold) per luxury/high food tile on the outer ring but that's not the case with the Shoshone. Really look hard for ways of getting "everything" in your 3 ring radius.
For anyone wondering why having a mountain in the 1-ring is important, it enables you to produce an Observatory which increase your science output by 50%. They're exceptionally powerful regardless of the VC that you're pursuing and should always be rushed. Gardens can be built in cities next to rivers and they provide you with a 25% bonus to great person production. Any extra Great Scientists/Great Writers/Great Artists that you can churn out are going to prove significantly valuable later on. Great Musicians not so much but I mean a bit of extra culture never hurt anyone. Rivers (and all fresh water) also grants you a ton of early food from Water Mills and Civil Service which kicks in long before Fertilzer does. Since growth = population and population = science expanding on rivers really is your best bet whenever possible. Planting a city on a hill grants it 2 base production and some extra combat strength whereas dropping a city on flatland nets you only 1. Sure, you can build a Windmill in them later on, but early production and defense are worth way more than a bit of extra lategame production. Expanding on/near luxuries is fairly obvious. They're 4 "free" happiness and excess luxuries can always be traded or sold as needed to the AI. Luxury trading is a great way to trigger "We Love the King Day"s and to net extra happiness but otherwise there's a ton of things that you can do with 240g/6gpt.
The Mid Game:
Now you have some workers and a steady stream of cash deals. It's time to grow. Spam farms on every reasonable tile in your cities. Growing really big really fast is essential. Trading Posts are too slow and their science upgrade comes too late for you to rely on that. We need a ton of science NOW. The only way to get that is with raw population.
Now, there are 2 basic ways to get population early on. The first is to use food caravans. I personally hate that option. My preferred method is to string "We Love the King Day"s all game long and to spam farms while my caravans and luxuries/strategics rake me in some cash. I then use that cash to buy CSes, pay people to go to war, buy luxuries for WLtK days, hard buy Universities + Public Schools + Research Labs, etc. Sea food trade routes are obviously insane and should be abused however. It's by far and away the biggest advantage of being coastal in my mind. I will always have multiple sea food trade routes active whenever possible.
To support that growth we're going to need happiness. My bare-bones advice is as follows. First of all, grab Circuses early. Granary - Library - Circus is no joke. You need to generate a happiness buffer fast because your population will explode in a bit and you'll find yourself struggling to support it otherwise. Beyond that, find a mercantile CS who has a luxury that you do not. Your sole mission in life is to forge and maintain an alliance with it. Yeah, it's probably going to cost you 500g because that jerk wants a Great Merchant or something equally unobtainable. Too bad so sad. You need that happiness buffer and since keeping multiple alliances can be rough I encourage that you just pick a single Mercantile one to focus on for the entire game. Obviously you can work at establishing relationships with others as well, that's fine, but you will need at least 1 Merc CS to pull this off properly. Finally, get Colosseums rolling fast and get the Circus Maximus at a reasonable clip. They, much like circuses, are basically required if you want to support unbounded growth.
Preventing War:
Now, the last thing that we need to address is the AI. They're going to want to kill you. Lucky for us the AI in this game is garbage. If you see an AI marching an army at you then they're in "war mode." Just pay him to DOW someone else who's nearby. It works something like 90% of the time once you start hitting turn 150 and whatnot. Otherwise just sell your gpt for a lump sum and get walls and a couple of archers/Comp Bows for defense. This is typically what you'll have to do early on since the AIs won't really be bordering each other just yet so getting them to DOW each other is difficult at best. Still, whenever I see someone moving towards me I can often pay them to DOW someone else. Have something on your borders to scout for advancing armies and just pay them to bother a nearby threat whenever you can. If not, hey, no big deal as long as you have some gpt and a friend.
Science Win Tips:
1) Spam farms, especially on tiles that have access to fresh water. Trading Posts take way too long to kick in and should only be built on Jungle tiles usually. Having raw population is just as good and stays relevant at every stage of the game. Don't feel bad about pumping out 6ish workers and spamming farms on everything.
2) Complete the Oracle before turn 80 if you want to secure it. Use it to rush Consulates. It's an insanely overpowered policy.
3) Fill your scientist, artist and engineer specialist slots as soon as your cities have 10 or more population and work them constantly. Universities, Guilds and Factories have 2 and Workshops, Public Schools and Research Labs all have 1 each. You want them all going as soon as you possibly can in each and every one of your cities. Like, your cities should all look like this eventually. Secularism is the stone nuts and will enable you to generate ludicrous sums of beakers by doing this.
4) Have your first 2 Spies steal techs from the tech leader/some warmonger who you know has more techs than you. You can open the demographics tab to view the current tech leader (look at "Literacy" at the very bottom) and otherwise you can keep an eye out for units and wonders to take a mental snapshot of where someone is in the tech tree. You can't build Artillery until you hit Dynamite after all. I like to steal my way to Workshops and rush buy them in my cities.
5) Build Gardens/The National Epic at a reasonable pace. Prioritize them over most tier 2 buildings (Opera Houses, Zoos, Windmills, Banks, etc.) and even things like Markets in non-trade hubs. You want that bonus rolling early. It loses an immense amount of value over time.
6) Plant Academies with your Great Scientists (GSes) and have your Capitol work them until you reach Scientific Theory. Save your GSes for bulbing past that. Popular tiles to plant Academies on include Cows, Deer and Plains/Grassland that don't have access to fresh water. Planting them on Hills will hinder your ability to grow and hurt your lategame production severly.
7) Complete the Porcelain Tower before the first World Congress vote happens. If you start on 135 and end by 160 that will usually be good enough.
8) Winning the World's Fair is essential for super fast wins. Always propose it at the first World Congress. You'll need at least 700 hammers to reliably take it down so plan to works mines/etc. accordingly. 8 turns after you win it pop your Great Writers (you should have at least 2) for 3000 culture total (or so). You should never need to build Opera Houses or above using this strategy. I just delete any Great Musicians that I spawn normally.
9) After you finish Scientific Theory beeline Radio and then grab Industrialization before moving on to Fertilizer and then Plastics. From there you can grab Satellites into Advanced Ballistics into Nanotechnology into Particle Physics.
10) Choose Order as your Ideology and open with 2 happiness policies. +2 happiness from Monuments and +1 happiness for Workshops/Factories/etc. usually. Your happiness goes FAST when the AI starts getting their Ideologies so you want a huge happiness buffer. It's not uncommon to suddenly lose 30+ happiness over the course of a few turns. Grab Worker's Faculties as your first Level 2 and hard-build Factories in all 4 of your cities asap. Otherwise focus on happiness and production tenets. Do not worry about grabbing the Level 3 science tenet; it's not especially valuable.
11) Have Oxford being built as you're researching Replaceable Parts. Time it so that they both finish on the same turn. Use the free tech on Plastics. Rush-buy Research Labs in all 4 of your cities if possible. Skyscrapers from the Order Ideology (-33% cost to buying buildings) will help with this a lot. Don't forget to work their scientist slots!
12) Building the Hubble Telescope will ensure that no computer will be able to challenge your science victory (SV) and so completing it should be made a priority. Bulb Satellites with a GS after Rocketry finishes and start producing it in your highest production city while another pumps out The Apollo Program. If you have/can afford a Great Engineer (GE) to rush it, by all means, do so. The best way to obtain one is to purchase one with Faith. If you picked up Consulates in the Patronage tree before opening Rationalism there's a good chance you'll naturally acquire enough faith in order to build one. Your alternatives include getting lucky with pantheons/faith-based natural wonders and/or producing Shrines and Temples reasonably early.
13) Buy GSes with Faith and use them to shave 8 turns off of your finishing time. 2500 gets you 2 and 5000 gets you 3. If you get 3500 just get 2 GSes and 1 GE to rush Hubble. If you get 2500 or less just get 2 GSes and hard build Hubble. You'll be sitting around waiting for Particle Physics to finish anyways so rushing it doesn't really accomplish anything.
Example sub-250 wins:
Blazing fast 217 win. Deity proof.
Sweet 224 win. Deity proof.
235 win despite early war with Assyria. Deity proof.
Decent 236 win. Deity proof.
Nice 238 win. Deity proof.
Easy 245 win. Deity proof.
To give you an idea, look at this. Yes, this is Deity. Sub 220 wins are possible with this strategy.

Pathfinder -> Pathfinder (skip if you have mining luxury resources not covered with jungles OR 3+ forests to chop) -> Worker -> Shrine (skip if you find a faith ruin past turn 20) -> Settler -> Settler -> Settler (if not rush bought) -> Granary -> Library -> Oracle if you have heavy production and can finish it by turn ~80 (skip otherwise) -> Caravan (skip if you get Oracle, build in your first expansion instead) -> National College -> Writer's Guild -> University (as it becomes available) -> Market -> Caravansary -> Artists's Guild -> Porcelain Tower (finish by the time the first World Congress vote happens)
Shoshone, unlike most civs, can frequently find themselves looking at starts such as this. You get a lot of early land and plenty of access to 2 production tiles. When paired with their ability to grab an early population ruin or two it makes sense to open with a Tradition-focused build and churn out some early Settlers. Your ruin control will allow you nab a quick Legalism anyways (i.e. Monument isn't needed) and if you find a ruin past turn 20 then your pantheon will be secured as well (i.e. Shrine isn't always essential). Focusing on Pathfinders, Workers and Settlers just plain makes a lot of sense. I mean, why wait when you can just do this?
Whenever possible rush buy things like Water Mill, Workshop, Stone Works, Lighthouse, etc. They're cheap and essential but your Cap has so much to build and so little time to pump everything out. You need your gold buildings up asap to power your economy and you need your Guilds online to flesh out your culture needs.
For what it's worth I've never found a good time to build the Amphitheater and so I basically never do. It's too expensive + useless to buy and it requires too many hammers to build.

Granary -> Library -> Caravan (assuming that you're building Oracle in your Cap) -> Walls*

Library -> Granary -> Walls*
*Walls should only be built if you're forward settling on an aggressive opponent such as the Zulus, Assyria, Aztecs, Rome, etc. You may need to go Library -> Walls in your forward cities if you're expanding into fearsome opponents and won't have much production early on (i.e. no time to go Library -> Granary -> Walls by turn ~80).

Settler;
Worker;
Worker;
Library in your 4th city if required;
You want a ton of Workers when you're Shoshone. Having 6-7 rolling is highly desirable and you're the one civ who doesn't need to buy tiles (very often) and who usually has a ton of sellables that they can improve immediately. I always steal one, make one and you can often nab one from a Barb camp. The rest you'll probably have to buy but that's not a big deal usually.

Tradition Opener - Legalism - Monarchy - Landed Elite (you should obviously go LE first if you're planning to grow for a bit)
Patronage Opener - Consulates (this assumes that you got Oracle or some form of extra culture generation)
Aristocracy - Oligarchy (note that it's not always possible to open Patronage before getting Aristocracy, that's fine though)
Rationalism Opener - Secularism - Humanism - Free Thought
Order -> Young Pioneers + Social Realism - Worker's Facilities - Skyscrapers - Five-Year Plan
(Hero of the People isn't bad either and you can always grab more happiness policies as needed)
Finish Rationalism before your last batch of RAs finishes. You can usually finish the tree off shortly after you grab Worker's Facilities. This is especially true if you win the World's Fair and pop a Great Artist to get a Golden Age at the same time as you get the bonus culture. Pop all of your Great Writers 8 turns later for roughly 1500 culture each. You may have used one earlier to get Secularism faster but that's fine. You should have at least 2 to blow which is 2 full policies at this stage of the game.
This build basically assumes that you get Oracle which is quite reasonable on Deity insofar as you have a moderate amount of production. Anything other than pure grassland/floodplains/jungle should do the trick really. You can start it somewhere around turn 60 and finish it somewhere around turn 80. That's going to be good enough a huge % of the time. If you don't get Oracle just hop straight into Rationalism once Tradition finishes (unless you're getting a bunch of bonus culture from CSes or a Pantheon).

Tech - Workers as needed - Caravan(s) - Water Mill - Stone Works - Lighthouse - Amphitheater - Market - Caravansary (trade hubs only) Garden - Shrine - Circus - Workshop - Colosseum - Temple
Buildings such as Universities, Observatories, Public Schools, Factories (assuming Order) and Research Labs should be prioritized above everything else. Beyond that you want to focus on happiness, growth, great person generation, gold and production. Culture gets the raw end of the deal and won't get much love if you're not actively pursuing a CV. You definitely can't ignore it though. My basic culture acquisition strategy is to grab quick Amphitheaters in my expansions (I rarely build it in my Cap) and use those + Consulates + Guilds + winning the World's Fair to cover my needs. I basically never build Opera Houses or above in my cities.

Pottery -> Mining (get this first if you have at least 1 mining luxury or 3+ forests to chop) -> Animal Husbandry -> Bronze Working/Masonry/Trapping if required -> Calendar -> Writing -> Philosophy* -> Bronze Working + any missing luxury techs -> Civil Service -> Sailing** -> Theology -> Education -> Construction*** -> Astronomy (if you have multiple cities and/or your Cap next to (a) mountain(s))-> Engineering -> Guilds -> Acoustics****.
*This should be done by turn ~60. That often means ignoring a luxury tech such as Masonry or Trapping. That's fine. You need to get a fast Philosophy for a fast Oracle. Between Calendar and either Bronze Working, Trapping or Masonry you be fine with happiness until turn ~75.
**Sailing shouldn't take more than 1-2 turns. Put it off until you have your NC + enough Libraries to pump it out without significantly hindering your sprint to Education. You're doing it wrong if it's taking you like 6 turns to churn it out.
***Pick this up as needed for happiness. You can go some games without ever building Colosseums so if you have plenty of luxuries just ignore the tech until you're forced to take it.
****Obviously you can beeline Acoustics after Education for social policy reasons if needed. Being able to open the Rationalism tree straight out of Tradition is a huge benefit if you're not going Consulates. So yeah, always try and make this happen if it's a possibility. No need to rush into the Renaissance otherwise.
This is basically your best bet regardless of the victory condition (VC) that you're pursuing. This strategy involves getting 4 very tall cities very quickly and amassing a ton of GPT to support them. From there you can win however you want. Bronze Working is worth grabbing early since you'll almost always have Iron and it's worth grabbing it to sell for 45g per. Engineering is useful for the extra Trade Route and Guilds is nice for getting your next Guild up and running. Ignore Archery whenever possible and simply use an upgrade ruin to grab an early Composite Bowman instead. It'll save you beakers and hammers.
Rough Ruin Priority:
The first faith > population > the first culture > unit upgrades > tech > gold.
The first ruin that you find is best used on population. You can only select the same option every 3 picks and since we want at least 2 of these it's important to get it first. Grab culture next to open Tradition up. Never take another culture ruin though. Grab an upgrade ruin next to get an early Composite Bowman. Next you'll want a second population and you can grab tech and gold as needed from there (tech > gold). The first ruin that you find past turn 19 is best used on faith to snag a quick and easy pantheon. Again, since you can't just chain the same option over and over you'll have to make due with tech and gold ruins as needed. Culture becomes rather worthless after the first so that stops being a realistic option in my mind. An ideal sequence would look something like: population (on turn 2) - culture - unit upgrade - population - tech - faith or something roughly along those lines. Finding 6ish ruins isn't difficult at all on Pangea maps against computers for what it's worth. Obviously if you only find 2 then you only find 2 and that's life.
Pathfinders upgrade to Composite Bows which are fantastic at clearing Barb camps for early city state (CS) quests and for staving early aggression off. I'm never unhappy to take 1 upgrade early on. It's usually enough to forgo Archery altogether in my experience since Comp Bows tend to ~3 shot most Barb Camps early on. Still, I'm not opposed to getting additional Comp Bows if possible either. They're incredibly useful during the scariest stages of the game.
Ruin Tactics:
Starting on turn 20 you can select 20 faith as a option for your ruins and so if you find one on turn 16 or later you're usually better off sitting and waiting for turn 20. This is completely safe if there's a nearby hill to provide vision but obviously it's risky if you're surrounded by jungle and can't see incoming scouts. At that point you have to make a judgment call. In the dark I'd opt to grab it and hope to find another but I mean it's your game. Population ruins should be given a similar treatment. If I'm growing in like a turn then I like to sit near a ruin and wait to grow before nabbing it. This is a fantastic way to spring straight to 5 pop to start churning Settlers out. Working 5x 2 production (hills, horses, most mining-based luxuries) produces a Settler extremely quickly (~7 turns) and given your massive starting land it's not unreasonable to have 5 workable ones right off the bat.
The Opening Turns:
The basic BO is to get 4 cities up and running with Libraries and Granaries so that you can rush out a National College around turn 100 so that you can start to grow big and strong. Steal a worker and improve everything that you can sell. Use that gold to buy workers, Libraries and defenses as needed.
Pathfinders are good versions of scouts/warriors but they take a long time to build. Still, you really need to get them out early on so that you abuse their ability to pick and choose your early game ruin benefits. I strongly recommend pumping out at least 1 because Shoshone typically doesn't need a super early Shrine to get a pantheon nor do they need a Monument to get early culture. You'll (virtually) always get a Pantheon and you'll (virtually) never have to wait very long for Legalism.
The first thing that we need to do is find ourselves a worker. Start by sending your Pathfinder (PF) exploring in a straight-ish line. Whenever possible walk over and/or end your turns on hills to maximize your sight. Don't worry about doubling back to check over your entire starting area; just keep trucking along looking for City States (CS)es and civs. When you meet your first civ you should strongly consider stealing a worker from him or her if they're within ~10 tiles of your Cap. Remember that your PFs are quite beefy compared to Scouts. They can take a shot or two from a city and still walk away with half of their HP. You can't eat 2 city shots + 2 warrior attacks but you can steal pretty much any relatively undefended worker and run away. A good rule of thumb is that you can survive "any 3 hits." Warrior hit + Archer hit + city hit, city hit + 2x Warrior hit, 3x Warrior hit, etc. will not kill a PF. Obviously stealing from a CS is easy since you can immediately make peace with them. The negative diplomacy modifier associated with starting an early war will quickly fade as well so there's basically no reason not to do it as long as you don't start more than one. Stealing a worker is one of the best and easiest ways to get ahead in the game.
Eventually you'll have 3 PFs running around looking for ruins, NWs, trading partners and CSes. If you find a religious civ early on then you can definitely skip the Shrine since 24-28 faith on turn ~20 is typically more than enough to secure a pantheon. Since you should have a worker by now you're basically just looking for NWs, all the civs and as many CSes as you can possible meet. Deity AIs get writing exceptionally fast so sell your embassy to each of them for 1gpt. That 210g will come in handy in a bit.
It's time to start pumping out a few Settlers. Lucky for us Shoshone gets fast + free population and usually has a few mines/2 hammer tiles to work. You'll hit 4-5 pop faster than any other civ and once you get there you can usually pop out 2 Settlers in 14-16 turns. That's pretty close to what Liberty manages. The last one can be built or bought depending on your gold situation. Just buy multiple workers instead if you decide to hard build all 3.
Once you have a worker or two back at home focus your efforts on improving everything that you can sell. This includes horses, iron, luxuries, anything. Horses and iron can be sold for 1gpt/per. Luxuries net you 6gpt. Ideally someone will offer you a declaration of friendship (DoF) at which point you can start selling things for lump sums of gold. Horses and iron are good for 45g/per and luxuries can get you 240g. Shoshone get a lot of land and what this means is that you'll usually have a lot to sell. Get it all improved asap and start generating some gold to buy a Settler and some Workers. Use those workers to improve more tiles and sell more luxuries and strategics. Abuse the fact that you get all of your resources in your opening borders at no cost. Whereas everyone else has to buy their way to luxuries you get them all automatically.
Disclaimer: Obviously you can get unlucky and be looking at bare land with nothing to sell. Shoshone isn't immune to that type of bad luck. My point is simply that they have a high probability of having immediate access to the vast majority of their resources. Whereas most civs need to buy tiles early on you can afford to spend that gold on other things.
Farming Workers:
Since this seems to confuse a lot of people, I'll briefly discuss farming Workers from AIs. When you find your first AI you'll want to look for one of their cities that still has unimproved tiles. Wait for a Worker to come by who can't be reached by many combat units in 1 turn. Grab it and quickly run 2 tiles away and heal. Pillage the tile if it was improved to ensure that more Workers will come back. A few turns later another Worker should come. After stealing 2 you can offer peace to the AI or more likely they'll offer peace to you. Just take it. 2 Workers is good enough. Sample:
I see a Worker. I see that the Warrior can't get to it in one turn.
I take Worker + Pillage tile to ensure that another Worker will come back for it.
Like moths to the flame...
All for Tich!
Barbarians:
This is an issue that arises often so I should probably address it. There's no one right way to handle Barbs in BnW. Sometimes you have plenty of nearby AIs who'll take care of any and all Barb camps for you. It's pointless to rush Archery in those spots. The only time Barbs give you fits (in my experience) are when you're isolated and when you randomly have 3 or more camps spawn nearby you. They'll still pester CSes and such a good % of the time but you can, on occasion, get absurdly unlucky and have them basically rally units at you even if there are other nearby civs/CSes. If you need Archery, take it. That's all that I can say really. It pops after a few turns and Archers are quick and easy to train/buy as needed. I realize that this isn't especially helpful, but really, I'm not sure what more people expect to hear. You'll have tons of scouting information from 3 Pathfinders so you yourself are going to have to make judgment calls about the Barbarian scum. I rarely find myself needing it since Deity AI stomp all over barb camps but if I'm isolated and surrounded by them then I'll obviously adapt.
It's also worth noting that Pathfinders upgrade to Composite Bows if you get a ruin upgrade. If you play one of those games where you find like 6+ ruins then feel free to grab a second Comp Bow (always get one with your third ruin). Use it to clear Barb Camps for CS quests, defend your Settlers, stave early aggression off, etc. You'll basically never need Archery as Shoshone.
City Placements:
Whenever possible expand on hills that have a mountain tile in their 1-ring radius, that have access to fresh water (i.e. a river) and that have a luxury anywhere in their 3-ring radius. That's obviously the "ideal scenario" but I mean that's what you should be looking for at all times. Having access to production and such is nice but I mean beggars can't afford to be choosers. Try to space your cities 6-8 tiles apart and do your best to avoid having an "outlier." Deity AIs LOVE to spam cities and it will be surrounded in no time and that will tick a lot of people off. Whenever you are lucky enough to have rivers nearby try and expand on them in such a way that computers will be forced to cross it in order to attack you. The river penalty combined with your hill bonus make taking your early cities extremely difficult. Take a look at this and see how it quickly became this a few turns later. No walls, no comp bows, just 2 archers and cities on hills behind rivers. Again, ideal scenario, sure, but it's still worth keeping in mind. Finally, remember that Shoshone can really abuse the 3 tile radius. Even though you won't get every luxury every time you'll still get most of them and the ones that you don't get should only be one quick tile purchase away. Normally you have to buy 2 tiles (~150 gold) per luxury/high food tile on the outer ring but that's not the case with the Shoshone. Really look hard for ways of getting "everything" in your 3 ring radius.
For anyone wondering why having a mountain in the 1-ring is important, it enables you to produce an Observatory which increase your science output by 50%. They're exceptionally powerful regardless of the VC that you're pursuing and should always be rushed. Gardens can be built in cities next to rivers and they provide you with a 25% bonus to great person production. Any extra Great Scientists/Great Writers/Great Artists that you can churn out are going to prove significantly valuable later on. Great Musicians not so much but I mean a bit of extra culture never hurt anyone. Rivers (and all fresh water) also grants you a ton of early food from Water Mills and Civil Service which kicks in long before Fertilzer does. Since growth = population and population = science expanding on rivers really is your best bet whenever possible. Planting a city on a hill grants it 2 base production and some extra combat strength whereas dropping a city on flatland nets you only 1. Sure, you can build a Windmill in them later on, but early production and defense are worth way more than a bit of extra lategame production. Expanding on/near luxuries is fairly obvious. They're 4 "free" happiness and excess luxuries can always be traded or sold as needed to the AI. Luxury trading is a great way to trigger "We Love the King Day"s and to net extra happiness but otherwise there's a ton of things that you can do with 240g/6gpt.
The Mid Game:
Now you have some workers and a steady stream of cash deals. It's time to grow. Spam farms on every reasonable tile in your cities. Growing really big really fast is essential. Trading Posts are too slow and their science upgrade comes too late for you to rely on that. We need a ton of science NOW. The only way to get that is with raw population.
Now, there are 2 basic ways to get population early on. The first is to use food caravans. I personally hate that option. My preferred method is to string "We Love the King Day"s all game long and to spam farms while my caravans and luxuries/strategics rake me in some cash. I then use that cash to buy CSes, pay people to go to war, buy luxuries for WLtK days, hard buy Universities + Public Schools + Research Labs, etc. Sea food trade routes are obviously insane and should be abused however. It's by far and away the biggest advantage of being coastal in my mind. I will always have multiple sea food trade routes active whenever possible.
To support that growth we're going to need happiness. My bare-bones advice is as follows. First of all, grab Circuses early. Granary - Library - Circus is no joke. You need to generate a happiness buffer fast because your population will explode in a bit and you'll find yourself struggling to support it otherwise. Beyond that, find a mercantile CS who has a luxury that you do not. Your sole mission in life is to forge and maintain an alliance with it. Yeah, it's probably going to cost you 500g because that jerk wants a Great Merchant or something equally unobtainable. Too bad so sad. You need that happiness buffer and since keeping multiple alliances can be rough I encourage that you just pick a single Mercantile one to focus on for the entire game. Obviously you can work at establishing relationships with others as well, that's fine, but you will need at least 1 Merc CS to pull this off properly. Finally, get Colosseums rolling fast and get the Circus Maximus at a reasonable clip. They, much like circuses, are basically required if you want to support unbounded growth.
Preventing War:
Now, the last thing that we need to address is the AI. They're going to want to kill you. Lucky for us the AI in this game is garbage. If you see an AI marching an army at you then they're in "war mode." Just pay him to DOW someone else who's nearby. It works something like 90% of the time once you start hitting turn 150 and whatnot. Otherwise just sell your gpt for a lump sum and get walls and a couple of archers/Comp Bows for defense. This is typically what you'll have to do early on since the AIs won't really be bordering each other just yet so getting them to DOW each other is difficult at best. Still, whenever I see someone moving towards me I can often pay them to DOW someone else. Have something on your borders to scout for advancing armies and just pay them to bother a nearby threat whenever you can. If not, hey, no big deal as long as you have some gpt and a friend.
Science Win Tips:
1) Spam farms, especially on tiles that have access to fresh water. Trading Posts take way too long to kick in and should only be built on Jungle tiles usually. Having raw population is just as good and stays relevant at every stage of the game. Don't feel bad about pumping out 6ish workers and spamming farms on everything.
2) Complete the Oracle before turn 80 if you want to secure it. Use it to rush Consulates. It's an insanely overpowered policy.
3) Fill your scientist, artist and engineer specialist slots as soon as your cities have 10 or more population and work them constantly. Universities, Guilds and Factories have 2 and Workshops, Public Schools and Research Labs all have 1 each. You want them all going as soon as you possibly can in each and every one of your cities. Like, your cities should all look like this eventually. Secularism is the stone nuts and will enable you to generate ludicrous sums of beakers by doing this.
4) Have your first 2 Spies steal techs from the tech leader/some warmonger who you know has more techs than you. You can open the demographics tab to view the current tech leader (look at "Literacy" at the very bottom) and otherwise you can keep an eye out for units and wonders to take a mental snapshot of where someone is in the tech tree. You can't build Artillery until you hit Dynamite after all. I like to steal my way to Workshops and rush buy them in my cities.
5) Build Gardens/The National Epic at a reasonable pace. Prioritize them over most tier 2 buildings (Opera Houses, Zoos, Windmills, Banks, etc.) and even things like Markets in non-trade hubs. You want that bonus rolling early. It loses an immense amount of value over time.
6) Plant Academies with your Great Scientists (GSes) and have your Capitol work them until you reach Scientific Theory. Save your GSes for bulbing past that. Popular tiles to plant Academies on include Cows, Deer and Plains/Grassland that don't have access to fresh water. Planting them on Hills will hinder your ability to grow and hurt your lategame production severly.
7) Complete the Porcelain Tower before the first World Congress vote happens. If you start on 135 and end by 160 that will usually be good enough.
8) Winning the World's Fair is essential for super fast wins. Always propose it at the first World Congress. You'll need at least 700 hammers to reliably take it down so plan to works mines/etc. accordingly. 8 turns after you win it pop your Great Writers (you should have at least 2) for 3000 culture total (or so). You should never need to build Opera Houses or above using this strategy. I just delete any Great Musicians that I spawn normally.
9) After you finish Scientific Theory beeline Radio and then grab Industrialization before moving on to Fertilizer and then Plastics. From there you can grab Satellites into Advanced Ballistics into Nanotechnology into Particle Physics.
10) Choose Order as your Ideology and open with 2 happiness policies. +2 happiness from Monuments and +1 happiness for Workshops/Factories/etc. usually. Your happiness goes FAST when the AI starts getting their Ideologies so you want a huge happiness buffer. It's not uncommon to suddenly lose 30+ happiness over the course of a few turns. Grab Worker's Faculties as your first Level 2 and hard-build Factories in all 4 of your cities asap. Otherwise focus on happiness and production tenets. Do not worry about grabbing the Level 3 science tenet; it's not especially valuable.
11) Have Oxford being built as you're researching Replaceable Parts. Time it so that they both finish on the same turn. Use the free tech on Plastics. Rush-buy Research Labs in all 4 of your cities if possible. Skyscrapers from the Order Ideology (-33% cost to buying buildings) will help with this a lot. Don't forget to work their scientist slots!
12) Building the Hubble Telescope will ensure that no computer will be able to challenge your science victory (SV) and so completing it should be made a priority. Bulb Satellites with a GS after Rocketry finishes and start producing it in your highest production city while another pumps out The Apollo Program. If you have/can afford a Great Engineer (GE) to rush it, by all means, do so. The best way to obtain one is to purchase one with Faith. If you picked up Consulates in the Patronage tree before opening Rationalism there's a good chance you'll naturally acquire enough faith in order to build one. Your alternatives include getting lucky with pantheons/faith-based natural wonders and/or producing Shrines and Temples reasonably early.
13) Buy GSes with Faith and use them to shave 8 turns off of your finishing time. 2500 gets you 2 and 5000 gets you 3. If you get 3500 just get 2 GSes and 1 GE to rush Hubble. If you get 2500 or less just get 2 GSes and hard build Hubble. You'll be sitting around waiting for Particle Physics to finish anyways so rushing it doesn't really accomplish anything.
Example sub-250 wins:
Blazing fast 217 win. Deity proof.
Sweet 224 win. Deity proof.
235 win despite early war with Assyria. Deity proof.
Decent 236 win. Deity proof.
Nice 238 win. Deity proof.
Easy 245 win. Deity proof.