Playing Tiny Chieftain as Sumeria, I am heading towards a 630 AD or 670 AD finish (depending on whether Fission shows up - there is a 69% chance with 4 civs). SGL with Mysticism, I believe, but it took me probably 20 turns before I got Masonry because I was looking for the Ottomans (they were the farthest away).
Since the early Middle Ages, I've 5 or 4 turned every tech; Industrialization was my last 5 turn tech. Good luck in the Middle Age Big Picture to have all 3 starting techs show up for the AI and draw Invention; mostly bad luck in the Industrial Age to have all 3 starting techs show up and trade for Steam Power and Medicine only to get Sanitation instead of Industrialization or Electricity.
I got a second SGL with the Republic slingshot and used it to finish the Colossus 16 turns early. But none since, so I had to hand build Cope / Newton. Cope was really slow and and SGL to build it probably saves me 5-6 turns of research overall; an SGL for Newton wouldn't really have done anything, since I was 4 turning all the Industrial techs anyway and with the hand build it is enough to give me 4 turn Atomic Theory @ 90% if I wanted.
Perfection in terms of luck on SGL (one for Cope) and Big Picture (Electricity) would have saved me 12 turns, I believe, putting my best score around 510 AD, which would have been #2.
I can only guess how Lord Emsworth got to 150 AD. That's 31 turns better than 510 AD, which would be my perfect luck score in this game. He did it with Russia, which makes me believe he got perfect / perfect luck. First, he must have had an SGL for Pyramids, and probably a second for Colossus and third for Copes. Second, he must have popped a settler in 3950 BC. Third, he must have had very good paths to the AI's to get their starting techs without wasting huts. Fourth, he must have gotten very good luck with techs from huts - techs instead of warriors, gold or maps, and including Monarchy to trade in the Big Picture. He may have even gotten the Russian triple slingshot (Philosophy to hit the Medieval Ages, then a free extra required Medieval tech after the Big Picture - Gunpowder or Education). Fifth, he must have had perfect luck on Big Picture trading - Electricity would have been his best pull. Sixth, a coal resource was already roaded and he had workers ready to railroad his core cities. Seventh, obviously, Fission as a part of the Modern Age Big Picture.
I think with Russia you can research as fast as with Sumeria even without the extra food in the city square. So the 30 extra turns can only be explained by hut popping luck, because I think I 4 turned maybe 90% of the techs. In the Ancient Ages, I took 6 turns on CB and I think 9 on Mysticism as my first two techs (to maximize SGL chances), but I was able to 4 turn several of the techs even in the Ancient Age (HBR, CoL, Philo, Lit I think).
There are 48 required techs (18 Ancient, 14 Medieval, 15 Industrial) + 2 necessary but not mandatory ones (Republic, Literature). You get 2 starting techs (50-2=48), plus on Tiny you can get a maximum of 3 starting techs from AI (48-3=45). Philosophy gives you a free tech (45-1=44). ToE gives you two free techs (44-2=42). You get a free tech in the Medieval, Industrial and Modern Age as a Scientific civ (42-3=39). If the AI's have perfect diversity in the Big Picture, they can give you 3 required techs in the Medieval Age Big PIcture (39-3=36), and 2 in the Industrial Age (36-2=34). That means the lowest possible number of techs you need to research without huts (or the Chieftain AI actually researching something for you) is 34.
At a minimum 4 turns per tech, that is 136 turns, or 170 AD. 4 turns per tech is impossible if only because of the Ancient Age research when you have 1 or 2 cities can't be done in 4 turns. The "true" number of possible turns without huts is more like turns 145-150, or 300-350 AD. The 15-20 turn difference between that and Lord Emsworth's 150 AD can only be explained by Russian hut-popping. Lord Emsworth's game is probably approaching the limit of what can possibly be done on that size map/difficulty, not unlike the 3800 BC Tiny Conquests. I don't know the maximum number of huts in a Tiny Pangaea, but popping 4 techs is probably the minimum.
I'm going to switch over to Russia and dump any game that doesn't pop a settler in 3950 and doesn't give me a SGL by Mysticism. I likely won't pop any huts until I find the AI and get the starting techs. I would consider possibly researching Philo as the last AA tech to get the triple Slingshot, which I've never done.
I don't know how many runs it will take to get into the 300's, which would be my goal. I'm hoping 50 or fewer.
@Moonsinger, start up the map generator. Grassland cows with at least 3 river tiles, please.