dont build up mil yet. your rivals are pretty weak
You have some (you could have more) experienced mounted units. From there, beeline to cavalery.
In the meantime start really the SE. You have to run scientists and farms not only in capital, but all cities with decent amoount of food.
Civil Services is then a priority
I second this. Skip to the end if you can't be bothered to read the long, rambling bit...
You're in no position to declare on anybody. You have no cats (don't even know construction), no elephants (Huayna does and they'll eat your Immortals) and no swords. With Huayna and Isabella both likely researching Feudalism due to the gamedate and war they're in, the only realistic target is Genghis, but you've far more important things to be doing than getting bogged down trying to take some walled cities off him with no siege support.
The most intelligent option from here would be harnessing the power of the SE to slingshot cavalry as early as possible, mass-upgrade your immortals and go on the rampage. Against AI longbows and pikes they don't even need siege support to tear through cities.
To do that you need farms, not cottages.
Goth should not be cottaged!
If you do go to war with Genghis (inevitable), it's going to get pillaged rotten. It's got huge food potential so can run LOTS of scientists under caste system, and it's also a great ironworks spot if the game lasts that long. There are other sources of dye and gems you'll have by then making it workshop/watermill a-go-go.
Guangzhou should also be farmed once CS is in for chain irrigation as that's another place that can run a lot of scientists under caste system.
Speaking of scientists, the academy was probably a mistake. For quick cavalry you need to
avoid machinery and bulb philosophy, paper, education and then liberalism yourself, whilst researching nationalism, music (if you can't trade philosophy for it) and gunpowder. You can then bag military tradition as the free tech and use education as trade-bait to backfill everything you skipped (it'll still be too early for any AIs to have it as they'll be preoccupied with the bottom part of the tech tree working through guilds and banking) before unleashing your horde. That means having a stockpile of 5 GS, ideally in the time it'll take you to self-research CS and Nationalism. Since you have no religion in your 4 best food cities and running Taoism would seriously tick-off your two potential friends (Huayna or Izzy), pacifism isn't going to help much unless you get busy with some Hindu missionaries.
With pacifism, the capital alone can generate 46GPP (100% scientist - even at the current size, you can run 5 just by abandoning the mines; growing will allow you to run as many whilst keeping that production once CS is in) which will seriously speed up the rate at which you can slingshot yourself up the tech tree. If you do go for Military Tradition from Liberalism, the next targets are constitution and then biology, since that combined with representation (and/or nationalism) will give you the beaker and drafting power to keep ahead of the pack as GS become progressively less valuable. GS can bulb printing press, chemistry and scientific method, all of which are on the way to biology, which makes the tech tree much shorter than it appears to a standard CE.
Settling Jumboville (sounds silly, but directly on the jumbos is probably best for that fishing village) is a good idea. I'd keep Machu Picchu when the time comes as it's actually a well positioned city. Desert copper is a pretty poor tile in the grand scheme of things so missing out on the ability to work it really isn't worth the raze/rebuild of a large mature city.
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So to recap:
Farm EVERYWHERE, especially Goth and Guangzhou (once CS is in) as they're two good food cities that can run a lot of caste system scientists.
Spread Hinduism once Beijing's finished it's monastery. Priorities are the capital, Shanghai, Goth and Guangzhou - your four best food cities.
Once you've bulbed philosophy with your next GS, revolt to pacifism and caste system (will doing 2 civics at once help on epic?). You'll need another turn of anarchy to pick a religion (either Hindu, which means you're friends with Huayna, not Izzy; or Tao, which means you're friends with nobody).
You'll potentially have 4 GS farms, so once you've got a scientist from one, fire all the specialists there to rapidly grow towards the happy/health cap, then rehire them and either grow-slow or stagnate.
Beijing's got the best hammer potential at the moment in terms of HE locations. Beshbalik and/or Guangzhou will be good naval bases further down the line once state property etc are available. With drydocks, having a coastal HE really isn't necessary.