550 AD spaceship launch, 700 AD victory.
Deity, Marathon, Standard size, Terra
I used Inca, but don't stop reading!
I honestly believe that many civs (possibly any civ) can meet the important milestones.
The quechua are great at fast conquest, but that will wreck your game. You need to start slower.
It's just a ~6 city "empire" in the first ~120 turns. (An axe rush could meet that timeline.)
Build 5 wonders.
Triple size to ~18 cities by turn 200.
Triple that to ~50 cities by turn 300.
Here's a closer look at what happened this game:
Start location: (not spectacular) 5 flood plains, a cow and 2 gold
(t12 - t24) Grab 3 workers from 3 AI.
Here my capital in yellow, surrounded by my first 3 victims.
I picked lincoln (orange) first because he has a gold (not that I can use it for a long time
and because he has a lot of forests.

World War I
(t48 - t77) I capture the 5 cities that I will keep.
Two more are conquered and given away for later re-capture.
(t96) Note: Hammurabi builds Stonehenge and has Holy cities. Conquer him after he gets a shrine...which he does 138 turns later.
Research
Mining, Wheel, Pottery, Writing...
(t105) Alphabet (free bronze, etc.) - Start pre-chopping.
*New Strategy for me.
Alpha allows me to drag everyone into war against DeGaulle.
I let him live as long as possible to share war diplo bonuses.
This helps make up for all the negatives for "declaring war on our friend"
In the screenshot:
Roosevelt (blue) and Peter (red) are left alive, but crippled. Holding cities I can't afford to keep yet.
Here you can see Mansa (gold) to my SW and Darius (light blue) to the NW. Darius has horses, so I leave him alone.
I decide to trek my whole army way up north to DeGaulle (dark purple) since he appears to have no metal/horses and he's great to pick on.

(t111) I need to capture one more expensive (distant) city because it has marble.
(t116) Math
This is the key tech to allow chops to be completed.
You must not over-expand to keep research moving until this point.
Next stop is Machinery/Civil Service (for macemen), then Education (oxford)
Wonders
(t134) Oracle MC (Mansa was already on Currency).
Over the next ~40 turns, I chop the usual wonders (G.Lighthouse, Pyramids, Hanging gardens, MoM),
but I skip Colossus this time. I was nice for high score on B&S map, but this is Terra.
Much later, I build Notre Dame figuring I'd need happiness badly with sushi and whipping, but it was not necessary.
This makes me think that the IND trait isn't very special for this game. I think Liz with PHI might be best.
(t155) Finally get Currency free
(t177) Went for machinery after MC again because Mansa is researching CoL for me
*New Strategy for me
(t180) I've always waited for macemen to start WWII, but realized that is too slow.
I start a sword war to take out one more fresh AI and clean up the AI that I left barely alive.
(194) Civil Service. I build up some cash and upgrade a couple Macemen.
I'll have Construction free soon and build cats + more maces
(t203) Paper. Peace. I now have 18 cities. (I built 3 settlers)
Darius was closest and the only western neighbor I planned to attack, so it seemed like the right time to take his land.

(t214) 1360BC - Education (I use a GS to bulb half--as usual. I like Oxford)
I never even was able to get a GS for an Academy in my capital. If only I had the PHI trait instead of IND.
I turn off research until Oxford is complete.
(t217 - t297) I use my Macemen and cats to go on a rampage to the east. I go after 3 AI and capture 27 more cities in 80 turns.
I want all wars done and be close to the domination limit before sushi.
Eternal peace.
Recently, I had gotten Biology free (t277) 730BC - from Liberalism,
and I picked up Communism (t290) for State Property and Kremlin.
My Empire stops ~10% short of domination. I figure there are border expansions and a couple New World cities I'll need yet.
I keep Asoka and Fred alive in order to give back cities if I get too close to domination. As it turns out, I never get that close and keep everything.

(t308) Medicine.
I go for Steel (Ironworks and leads to Railroad) and delay Sushi -- because Mansa will get me Corporation free.
(t315) 350 BC Sushi.
I produce execs in 1 turn by whatever means possible. Sometimes whip with 0/200, or use overflow, or quite often chop the last forests around.
I also try to make sure they can travel to a city in need in that same 1 turn.
I work my high-food, Globe Theatre city hard.
(t330) 200 BC Railroad. Mining Inc
Now that the wave of sushi execs has moved across the continent, I start the next wave of mining execs.
Each wave takes ~25 turns--but they overlap...so starting at t315 there was about 40 turns total for corp spread.
(t339) The last tech I really need ASAP is Assembly Line (factory+ coal plants)
I turn off research to pay for corp expansion and build up cash. I'm waiting for free Physics from Mansa.
This is probably the last tech I'll get free. Maybe Rifling yet. I will have built up so much cash,
and my corp-fueled empire's research will explode by then.
(t361) Finally Physics free
*New ground. I've never done a space race with this size empire and both corporations, so I'm winging it.
However, the game practically plays itself from here.
I decide that refrigeration is not needed at all, but I want Superconductors (for labs).
So I go the long way thru Plastics and Computers, but my research is so fast, I get there...
(t378) Superconductors
(t384) Rocketry. Build Apollo fast in the Ironworks city.
(t403) 515 AD. Ecology. Research is complete !
Here's where I didn't plan properly. I could have planned better and launched in 5-6 turns instead of 7.
Or, if I'd planned really well and saved a couple more forests from way back, I could probably do ~3 turns or less from tech complete to launch.
(t410) 550 AD. Launch!
Click End Turn 30 times.
Deity, Marathon, Standard size, Terra
I used Inca, but don't stop reading!
I honestly believe that many civs (possibly any civ) can meet the important milestones.
The quechua are great at fast conquest, but that will wreck your game. You need to start slower.
It's just a ~6 city "empire" in the first ~120 turns. (An axe rush could meet that timeline.)
Build 5 wonders.
Triple size to ~18 cities by turn 200.
Triple that to ~50 cities by turn 300.
Here's a closer look at what happened this game:
Start location: (not spectacular) 5 flood plains, a cow and 2 gold
(t12 - t24) Grab 3 workers from 3 AI.
Here my capital in yellow, surrounded by my first 3 victims.
I picked lincoln (orange) first because he has a gold (not that I can use it for a long time

and because he has a lot of forests.

World War I
(t48 - t77) I capture the 5 cities that I will keep.
Two more are conquered and given away for later re-capture.
(t96) Note: Hammurabi builds Stonehenge and has Holy cities. Conquer him after he gets a shrine...which he does 138 turns later.
Research
Mining, Wheel, Pottery, Writing...
(t105) Alphabet (free bronze, etc.) - Start pre-chopping.
*New Strategy for me.
Alpha allows me to drag everyone into war against DeGaulle.
I let him live as long as possible to share war diplo bonuses.
This helps make up for all the negatives for "declaring war on our friend"
In the screenshot:
Roosevelt (blue) and Peter (red) are left alive, but crippled. Holding cities I can't afford to keep yet.
Here you can see Mansa (gold) to my SW and Darius (light blue) to the NW. Darius has horses, so I leave him alone.
I decide to trek my whole army way up north to DeGaulle (dark purple) since he appears to have no metal/horses and he's great to pick on.

(t111) I need to capture one more expensive (distant) city because it has marble.
(t116) Math
This is the key tech to allow chops to be completed.
You must not over-expand to keep research moving until this point.
Next stop is Machinery/Civil Service (for macemen), then Education (oxford)
Wonders
(t134) Oracle MC (Mansa was already on Currency).
Over the next ~40 turns, I chop the usual wonders (G.Lighthouse, Pyramids, Hanging gardens, MoM),
but I skip Colossus this time. I was nice for high score on B&S map, but this is Terra.
Much later, I build Notre Dame figuring I'd need happiness badly with sushi and whipping, but it was not necessary.
This makes me think that the IND trait isn't very special for this game. I think Liz with PHI might be best.
(t155) Finally get Currency free
(t177) Went for machinery after MC again because Mansa is researching CoL for me
*New Strategy for me
(t180) I've always waited for macemen to start WWII, but realized that is too slow.
I start a sword war to take out one more fresh AI and clean up the AI that I left barely alive.
(194) Civil Service. I build up some cash and upgrade a couple Macemen.
I'll have Construction free soon and build cats + more maces
(t203) Paper. Peace. I now have 18 cities. (I built 3 settlers)
Darius was closest and the only western neighbor I planned to attack, so it seemed like the right time to take his land.

(t214) 1360BC - Education (I use a GS to bulb half--as usual. I like Oxford)
I never even was able to get a GS for an Academy in my capital. If only I had the PHI trait instead of IND.
I turn off research until Oxford is complete.
(t217 - t297) I use my Macemen and cats to go on a rampage to the east. I go after 3 AI and capture 27 more cities in 80 turns.
I want all wars done and be close to the domination limit before sushi.
Eternal peace.
Recently, I had gotten Biology free (t277) 730BC - from Liberalism,
and I picked up Communism (t290) for State Property and Kremlin.
My Empire stops ~10% short of domination. I figure there are border expansions and a couple New World cities I'll need yet.
I keep Asoka and Fred alive in order to give back cities if I get too close to domination. As it turns out, I never get that close and keep everything.

(t308) Medicine.
I go for Steel (Ironworks and leads to Railroad) and delay Sushi -- because Mansa will get me Corporation free.
(t315) 350 BC Sushi.
I produce execs in 1 turn by whatever means possible. Sometimes whip with 0/200, or use overflow, or quite often chop the last forests around.
I also try to make sure they can travel to a city in need in that same 1 turn.
I work my high-food, Globe Theatre city hard.
(t330) 200 BC Railroad. Mining Inc
Now that the wave of sushi execs has moved across the continent, I start the next wave of mining execs.
Each wave takes ~25 turns--but they overlap...so starting at t315 there was about 40 turns total for corp spread.
(t339) The last tech I really need ASAP is Assembly Line (factory+ coal plants)
I turn off research to pay for corp expansion and build up cash. I'm waiting for free Physics from Mansa.
This is probably the last tech I'll get free. Maybe Rifling yet. I will have built up so much cash,
and my corp-fueled empire's research will explode by then.
(t361) Finally Physics free
*New ground. I've never done a space race with this size empire and both corporations, so I'm winging it.
However, the game practically plays itself from here.
I decide that refrigeration is not needed at all, but I want Superconductors (for labs).
So I go the long way thru Plastics and Computers, but my research is so fast, I get there...
(t378) Superconductors
(t384) Rocketry. Build Apollo fast in the Ironworks city.
(t403) 515 AD. Ecology. Research is complete !
Here's where I didn't plan properly. I could have planned better and launched in 5-6 turns instead of 7.
Or, if I'd planned really well and saved a couple more forests from way back, I could probably do ~3 turns or less from tech complete to launch.
(t410) 550 AD. Launch!
Click End Turn 30 times.