So here's an overview at 2300 BC. I have 5 cities. Delhi, Bombay, and Seoul are the legendaries. Pataliputra will be a dedicated pretty nice Great Artist farm with three big food resources (fish offscreen).
I'm amused at using religions as a faux Creative trait here. Seoul is the Buddhist holy city for a quick border pop. Bombay already did the same. Just founded Confucianism in Pataliputra to pop its border quickly, and will send its missionary to Vijay to pop that border.
The "C" is my next city (Delhi about to whip a settler for it) and will have to use a Caste artist to bring the stone online. Patali also ran scientists to pop my first Great one (in order to outrace the Oracle and Stonehenge Prophets).
Oracle to Civil Service in 1825 BC. I also built Stonehenge in Seoul. Hadn't planned on it, but I saw it was still available and I had stone. Chopped one forest and then it was whippable at no risk, so I did so. 60 base hammers for 17 culture after doubling is a fine deal.
The biggest problem: HAPPY CAP. No Mining or Hunting happy resources within reach. But FOUR Calendar resources, so I went there right after Code of Laws. Calendar wasn't even enough to keep up with the high-food legendary cities, so then I also went straight to Drama (1450 BC) and ran some culture slider.
The other biggest problem: worker labor. I dedicated 3 then 4 workers to each legendary city which barely kept up with growth. Priority one is to grow each legendary as fast as possible and grow onto all its cottages. If I want to win by turn 245 (1000 AD), then I want towns by about turn 205, meaning to have each cottage planted and worked by turn 100. The other cities pretty much did nothing but build and whip workers for the legendarys until about 500 BC.
Music in 1050 BC. Next was Theology, both for the religion and to build the AP. Then Metal Casting, yeah forges will pay off to usefulness by the end of the game. Filled in Iron Working, then straight on up to Liberalism.
Pyramids in 1025 BC, and Representation mostly for the happy (only Pataliputra has any specialists.) Delhi continued on the Hanging Gardens, while another city (Varanasi) built non-critical wonders: the Apostolic Palace, Sankore, and later Spiral Minaret. Seoul added the Parthenon, as much for its base culture value as the effect.
Great Person #1 was a Scientist from Patali for Delhi's Academy. I think this is the right play - we did hit Bureaucracy early and Delhi has lots of early villages, plus it is 4 culture.
#2 an Artist from Patali, settled. So did the Music artist.
#3 was the Great Engineer from Delhi (Pyramids/HG/specialist) for Sistine.
I reached Liberalism at the early date of 245 BC. That is without any lightbulbing at all! And just one Academy, and fairly minimal use of Rep specialists. The big Bureaucratic capital pulled most of that.
Sure, Liberalism can come faster by bulbing, but what good does that really do? Free Speech needs base culture production and towns, both of which take time. Rather, I've conserved the cheap Great People slots for when they can all just be Artists. As I mentioned before, getting the Great Artists early doesn't matter since they just bomb Great Works anyway.
I went out to 10 cities total to have a little wiggle room on building the 9 of each temple. The settlers were nearly free anyway as whips from megafood Pataliputra. Calcutta, Madras, and Lahore each have one 6-food resource, one metal resource, and 3-4 hills. That's quite sufficient for temple building.
The three legendarys are already fully grown and working cottages on every tile including plains. That was a major project and a big key to a fast finish. I stayed off the whip hand, except at Delhi once or twice when it outgrew its improved tiles even with 4 dedicated workers. I looked ahead and saw the cities would hit the health cap around size 17, so leveled off there instead of pushing to a full 20. And any more laborers by this point could not work cottages to towns before the end of the game.
Whether to cottage hills or mine them is an ongoing question. I think the right answer is to work them last, mining them, since by then a new cottage will not mature to a town. If you somehow cottage a hill early enough that it will mature, maybe being worked by a helper city, do so. But on this map there were plenty of plains cottages to work instead of the hills. So I worked and grew the cottages, adding the mines later.
No city besides the legendarys ever got a single cottage. There was no time during the research phase to even build them let alone mature them, and of course they do nothing at all once you go culture slider. The only job of the outside cities was to build missionaries and temples, and all they need for that is some food and hills. They did not even build forges or libraries.
Liberalism went for Divine Right. I've experimented with a few different paths, and I think this is the right way to do it. Divine Right and Nationalism are actually just about the same beaker cost, since DR has no arrow prerequisites but Nat has two for a 40% discount. You do want both techs, but DR helps more sooner, to get Islam spread started and the Spiral Minaret. Nationalism doesn't do a whole lot just yet - both Taj Mahal and Hermitage are worth building but can wait until after the massive cathedral construction phase.
The other potential Liberalism target is Democracy. Is that worthwhile? I'm pretty sure that the answer is only if you do not have the Pyramids. Universal Suffrage is essential. But if you already have US, then despite what I've written before, just Emancipation and Statue do not pay back the extra research cost into a faster finish time. And also despite what I've written before, Liberalism to anything deeper like Biology or Medicine (Sushi) or Radio is way too much extra unnecessary research.
With Liberalism now in, the research phase is over. I immediately went to Uni Suffrage to start cash rushing, and Free Speech, plus Caste since Patali needs artists and whipping is not in demand now with cities growing and cash rushing available. I did build Sankore to keep some trickle research going at 0%, which first did Currency, then Nationalism as usual.
And yes, I have all seven holy cities. That did take a bit of luck in capturing Buddhism from Korea, and landing Hinduism even with Poly as my second tech.
On the scoreboard you can see Willem researching Construction and Pericles researching Alphabet, both of which I eventually traded for.
Great People #4 and #5 were Artists from Patali, both settled. GP #6 came from Seoul (the Stonehenge city) as a coin-flip Prophet. Sure, do the Hindu shrine, it is 9 culture with Sistine (hey, 45 after multipliers) plus the cash and AP hammers.
I've discovered that the biggest logjam in speedy culture is spreading all the religions by missionary. That limit of 3 per religion really chafes, and tying up one slot in a build queue for 4 to 6 turns is just terrible. So the sharpest chainsaw to cut through that logjam is cash-rushing missionaries. I spent as much cash as possible on buying missionaries (though never at the empty-box penalty), and even then ran up enough surplus cash a few times to buy about three cathedrals.
In 250 AD, turn 190, I was finished with missionaries, all 7 religions to at least 9 cities.
At this point, do I keep buying cathedrals? One costs 1350 gold. Of that 1350 commerce, about 1200 would come from the legendaries. That 1200 commerce could be 1200 + 300% = 4800 culture instead. If I buy a cathedral now, it gives about 30 turns of +50% culture before the city would finish building the 7th cathedral normally. 180 base culture x 50% x 30 turns = 2700 culture. Not enough. Stop buying cathedrals and go culture slider now. In fact I might even be a hair late on that.
I stayed at 100% culture slider the whole way, never needing even 10% cash, supported entirely by a couple cities on Wealth and by selling old techs to the AIs for 50 gold each. Nationalism came in after 30 turns of 0% research by Sankore and a few scientists. Delhi built the Hermitage just because it was the first to finish its cathedrals. I continued 0% research to Machinery - Printing Press, now faster with scientists in side cities that had finished their temples. Delhi also added a late Mausoleum just because it could and just ahead of the Taj Mahal, and also a very late Statue of Zeus with imported ivory.
0% research continued to Guilds - Banking (Mansa had come up with Feudalism to trade me). Mercantilism was definite - the free artist was worth more culture than the delta between foreign and domestic trade routes. Also got Economics and used the merchant for the 1-man Golden Age.
When the last cathedral and Taj completed in about 700 AD, I left Org Rel for Pacifism. All the rest of the Great People (numbers 7 through 11) came as Artists from the farm and went for Great Works.
Now the legendary cities were truly monsters. The full seven cathedrals, 10 or more towns each, and several early doubled wonders. Delhi passed 1800 culture/turn! and the other two hit about 1400. Here's one last overview as I bomb the 5 Great Works.
And that would be a cultural victory in 940 AD. 239 turns on Epic speed. I am satisfied.