Just submitted a game for this, won in 1465, so I missed first on the tables by 23 turns. I cost myself maybe 2-5 turns with little mistakes I think, just didn't have really good luck with leaders, and so couldn't challenge what's a really good date already there. One SGL from Masonry (I think) which was used for Pyramids, one from somewhere in the late middle ages, and one from theory of gravity, which was researched on the same turn as I reached 400 shields, letting me build Newton's, Sistine and JS Bach's on consecutive turns. Finished up at 153cpt I think.
The start:
The finish:
I could run 94 spt with zero growth, and either grow/starve by increasing shields by 4 and decreasing food by 2 or vice-versa. Max shields was 102 at -4 food. Finding oil with refining increased the stable spt to 96, the max to 104.
The builds:
Palace: 3950BC
Temple: 3450BC
Pyramids: 3100BC (SGL) - slight mistake, I didn't change builds via big picture when I got the SGL, so this and the next few builds should have all been 1 turn earlier.
Colossus: 2070BC
Oracle: 1375BC
Library: 1325BC
Mausoleum of Mausollos: 1025BC, triggering GA - looking at this now, I wonder if building Oracle-Mausoleum/GLib-Colossus to trigger tha GA much earlier would have been feasible. Might be one to test.
Hanging Gardens: 800BC
Great Library: 550BC - Again, I might need to test this. I think I worked out that I could build HG-GLib one turn faster than GLib-HG, due to how many spt I had at the time. I didn't actually work out whether the earlier doubling of 6cpt instead of 4cpt would offset that, and my GA ended one turn before GLib completed, so I might have stuffed up the original calculation anyway
Cathedral: 530BC
Colosseum: 490BC - Not enough cash to build both in 1 turn unfortunately
Knights Templar: 150BC - This build looks very slow compared to the next 2, I think I snuck in a couple of settlers after the colosseum, as I was still an OCC at that point.
Temple of Artemis: 260AD - Already had education by the time this finished, so it needed to be built then.
University: 270
Statue of Zeus: 340 - Took a while to get hold of Ivory, Korea had it, but didn't have their Ivory city connected to the rest of their empire, and therefore it couldn't be traded. Their Ivory city actually flipped to me before they connected it.
Shakespeare's Theater: 510
Copernicus' Observatory: 640
Heroic Epic: 650 - I took my crusaders and ancient cav off to play just before completing shakespeare's, and I received a 2nd MGL a few turns into the heroic epic build, and so changed it to cope's, and saved the MGL.
Newton's University: 780
Sistine Chapel: 790 (SGL)
JS Bach's Cathedral: 800 (SGL)
Magellan's Voyage: 930
Factory + Coal Plant: finished in 980. Lack of cash and having to find and hook up coal delayed this 3 turns as well
Universal Suffrage: 1070 (9 turns of growth, as I couldn't afford more than 3 turns of starvation at the time)
Theory of Evolution: 1130 (6 turns of starvation)
Smith's Trading Company: 1200 (7 turns of growth)
Hoover Dam: 1265 (8 turns of starvation)
At this point I was out of builds, as I didn't have enough cash to get 5 stock exchanges. I detoured my research for 4 turns to get Espionage, and the AI eventually researched Military Tradition for me. If I made more effort to expand to near the dom limit, my research would have been faster, and I would have reached the modern age before running out of builds.
Wall St: 1305
Intelligence Agency: 1325
Military Academy: 1375
Apollo Program: 1405 - Korea had been wiped out much earlier, Trading via big picture gave both Byzantines and Greece Rocketry, which left me a 3/4 chance of my freebie giving a culture build. I got space flight.
Research Lab: 1410
Finished up at 20024 culture, 153cpt. Looking at the hof tables, this is my fastest ever 20k, and it's the first time I've ever had an SGL with my first tech researched. So it's not too bad.