Here's my start, after ten or so map rerolls looking for something decent. There's river, enough resources including incense for culture, and coastal access allows the Sydney Opera House later.
I started with a scout, which on a large map dominates a monument start. The goodies from ruins make a big jump start for the snowball.
Like that, my favorite ruins result. That accelerates the Liberty worker by quite a bit (both directly and by getting the Liberty opener sooner), which came on turn 16. This is so important that I rejected and rerolled maps that didn't provide this by about turn 20.
My warrior also found a ruin for a free upgrade, which is bully awesome for Greece. That makes not a 7-strength spearman, but 9-power hoplite! Importantly, a hoplite is strong enough to disperse a barbarian camp all on his lonesome, clearing bad guys and earning gold.
Anyway, that shot also shows my neighborhood. Looks really nice: lots of rivers, plenty of resources, including lots of incense for cultural monasteries and for selling to AIs.
My build order was pretty standard, scout - monument - granary - scout - archer. Technology was Pottery - Mining (which then got popped from a ruin) - Archery - Animal Husbandry.
A ruin for a big score of 100 gold came on turn 16. What do most empires do with a pile of gold this early? It's not quite enough to buy anything good; a worker is the best hammer/gold value but that takes 310 and is somewhat redundant with the Liberty worker. Buying a city-state wears off quickly.
But not for Greece! I instantly bought 40 influence with Sydney. Bam, +2 food in the capital right away and Greece's ability means I have 20 turns to accumulate another $250 to refresh it. I got that pretty quickly, with a little help from a Siamese loan, upgrading Sydney's friendship to allied status on turn 28.
More ruins followed: a population increase, more gold, and more culture on turn 26. That accelerated into the Liberty settler policy just as my archer was built.
Lots of good land there. Where to settle? My settler journeyed for a while, then picked...
... this spot. Because of the Marble. Athens being coastal would require a second strong wonder city to share the load. Athens would eventually get most of its land tiles filled up with landmarks, so couldn't be a top hammer producer in the later game. But does Sparta look productive enough? Yes. It has 11 hammer tiles: four forests, three horses, two hill sheep, two other hills. And all those river plains will add up to a few hammers when farmed.
After the four starter techs, what now? There were a ton of competing priorities. Calendar to start selling incense; Masonry to build the Pyramids and improve marble; up to Mathematics for the Hanging Gardens; and at some point Writing. Of them all, I guess Calendar is the most snowbally, then Masonry, Wheel, Mathematics. The production department was a second worker at Athens (the first traveled to Sparta), then scout - archer - archer - warrior - worker - water mill - settler - Pyramids.
Check out those gold-filled piņatas rival leaders. I wasted no time putting that gold to work for myself, selling each set of incense and horses right away as they got connected. I wasn't going to use them soon. That gold went towards a second maritime city-state alliance with Genoa. And I popped barbarians near each of Sydney and Genoa, scoring 12 influence for 24 more turns of alliance with each.
Culture brought me my fourth social policy on turn 49, after the usual Liberty beginnings. The Classical era for Piety wasn't open yet, but I didn't really want more Liberty. The production and happiness policies are quite weak in a culture game (or anything other than max ICS), and the Golden Age policy wants to wait. So I opened Tradition now. And the next policy on turn 65 added Aristocracy for the wonder bonus, perfectly timed with Pyramids construction.
My ally Sydney had a barbarian camp nearby, and this was the first time I was poised to pull this trick: don't clear it, but let it keep spawning barbarians to farm for influence. That went well for quite some time. And then I pulled this really dastardly move:
I blocked the escape path of Sydney's worker, letting the brute capture it! Retrieving the worker meant finally clearing the camp, but that was fine. I now had 143 influence with Sydney thanks to the barb farming and an easy quest (find England). (Do the math and that is 166 turns of alliance for Greece. 
) With influence already virtually maxed, I kept the free worker for myself.
Research continued to Philosophy, then Horseback Riding. A big map means lots of barbarian activity, and a horseman would help a lot.
Athens got the Pyramids on turn 70. Hadn't intended to think about the Great Library, but couldn't help myself. With Aristocracy, it was only 85 base hammers more than a regular library. And it would sling Civil Service fifteen turns ahead of otherwise, boosting farms immediately, and also entering the medieval era boosts the culture yield from two city-states.
