Ok first submission for me is 1415AD. I'm not sure if I can beat it but I'll be giving it a go. There are a few things that I will change.
I played as the Ottomans as I said in an earlier post. The starting position was one tile away from the coast and when I moved into position, I found that as well as the couple of cows, I also had a wheat tile and there were only two coastal tiles, both of which had fish. I was going to need those food tiles with mountains rather than hills as my primary source of shields. Although there was only one bg and no immediate luxes, I knew that I would have to play this through when this happened:

The main reason for playing the Ottomans was to have the opportunity of getting the Pyramids so early on.
It didn't stop there. I got three more SGLs in the BCs for Philosophy, Construction and Printing Press. I also got one more much later on for Electricity. The Philosophy one gave me an early GLib after I had finished my MoM prebuild.
Research was a problem. The land around my capital was not too good. I have changed my next batch of saves to generate 4byo maps rather than 3byo. There were simply too many mountains to get a nice ring of cities with enough food in my core. I think I should also have chosen wet-that gives more rivers, doesn't it? There was also a distinct lack of luxes. I had just one source of one luxury so happiness was an issue. I'd rather be spending the cash on research rather than the happiness slider and building units rather than cathederals in my core. Maybe the latter was an error-not sure. Still, if you are only going to have a single lux, which one would you like? Ivory!
The tech pace was so slow and the AI so backward that I could have done with some scientific ones to get a move on. There were times when my 20K city was not building any cultural buildings!!!!!
Another mistake: I was far too peaceful for far too long. It was only when I found that I didn't have coal that I decided to start a war. I researched M-Trad, got a half a dozen Sipahis and took the Mongols outpost with sources of coal and iron. (It was far too corrupt to build the iron works in though.) The Mongols eventually showed up with some nice shiny stacks of Keshiks and I soon got what I was after:
When the Zulu cut off my coal outpost by expanding their cultural borders, I also declared on them. I liberated some gems but went no further because the Maya had also declared on me. The Maya gave me some nice silk towns plus some good science farms, although I was too late to put this land to good use. Anyway, I find fighting a defensive war easier for farming MGLs. You can bombard incoming troops until they are redlined, use your elites and withdraw them back to safety using your roads. When the Aztecs also declared on me, I had MGLs coming out of my ears. The only drawback was that turns take so much longer when you are fighting stacks of troops every turn. I ended up with 12 unfilled armies.
So next time around I will:
- Have more rivals including some scientific ones.
- Have a younger map for less mountains.
- Go to war much earlier, both for Heroic Epic and for more cities. I've chosen Persia this time for those fantastic Immortals.