jesusin, contender. Goal: fastest cultural victory. Result: 1525AD cultural victory.
Early game
Settling in place would kill seafood in the W, so moved my Scout N-NW. No seafood, marble and hills... I settled on Corn for a supercapital. First worker came in ultra-early.
High commerce map. Lots of happy resources too.
Produced Worker-Warrior-WB-Warrior-Settler. The WB went away exploring.
It should have been Worker-WB-Warrior-Warrior-Settler
Researched Mining-TW-Myst-MAson-Pott-PH-Writing-CoL-Alpha-Currency
Failed CS sling 1600BC. I should have used Oracle for CoL.
1000 BC Stats: 3 cities, 15pop, Set, 2workers, 3units(3War), 1 strategic resources, 2 luxury resources, 3 health resources, 0 great persons, 0 world wonders, 0 national wonders, food/production/commerce=40-18-96, 71 bpt at breakeven, 9 culture per turn, 3 great person points per turn, 20 gold, Gra, Lib. 1 religions, 5/6 cottages used, 15 Techs: Alpha, CoL, Mason, no BW. 0 civs killed. 3 hours played.
3 cities + 1 Settler at 1000BC in this map is too few. I should have expanded faster. This is the biggest mistake in my game.
Cities
Capital on Corn, Legendary through cottages and a few selected WW (Parthenon, Sistine's, MoM).
02 1N of Gold, Legendary through cottages.
03 E with fish and sheep, auxiliary that worked the capital cottages for most of the game.
04 far N, with Fish, Sheep and Stone. Moai. Legendary through sea-tiles and 1 WW (Taj Mah).
9 cities in all.
GPFarm in the Western island with Fish, Sheep and 2 farmed FP.
Single-tile double -seafood-resource in the East.
Medium sized mistakes
03 started a Library for Academy, but capital run faster and finially got a late GS in the capital instead (500AD

).
I missed the Gold site in the Eastern continent.
Music raze lost by 1 turn.
I went for Islam in the end for a 3rd religion. Should have gone for Theocracy much sooner. A 4th religion would have come in handy.
Key data
Liberalism 780AD. Too late for the map.
Revolution to Castes+Pacif 880AD. Late religions meant slow cathedrals and a delay on GA generation.
Culture 1525AD. 3 religions, Multipliers 4.5-3.5-3.5, bombs 1-5-7, base cpt 220-160-130, 1GS Acad, 1GA GAge, 13GA bombed, total 15GP, none of them for free.
Curiosities
Privateers started to appear around 1500AD, so I decided to win the game soon after that

Peaceful game.
5 Workers.
Less military units than cities.
All GP were obtained at 100% probability.
Your last GA shouldn't be born in another island, or travel time will delay your victory.
EDIT: Without Pottery, Masonry and The Wheel, I could have completed the CS sling. Not sure if that would have been better than the game.