Ok well I did a turn 197 with NO OBSERVATORIES ( haha ) with Order with this modded civ, the halfings.
Their ability is basically to start with a medical lab in every city. They also have a water mill that gives +1 food and +1 culture to every river tile, and it counts as a culture building for tradition purposes ( so if you build monument first, then you get free water mills.
I just tried a random liberty/tradition mix type game to see how I could abuse this and it randomly finished at less than 200 with no observatories.
I gotta say, this is a pretty good civ yep
Says turn 198 no pic because dumb AI jammed an automated worker into my capital to prevent me from adding spaceship parts. Wow, just wow.
Spoiler :
1559 bpt with 167 pop seems a bit low to me. Why weren't you working science in all your cities?
Also, why not just dow the civ to force their worker out?
This was a super bad game too, no observatories is obviously awful.
But also, Greece and Kamehameha nearby always DoWing me, and all the AIs hating me right away for spamming 6 cities in the early game. So almost no RAs until late game.
But my cities were insane. I went for workshops before universities, don't know if that's a mistake. I did get Leaning Tower and Sistine Chapel and crushed World Fair solidly, but I still didn't even finish Rationalism. I finished Liberty though, to get a great scientist. No idea how much culture I would be having late-game.
My counterspy only got 1 guy, none of my spies managed to get any techs and basically I couldn't even attempt a single city-state coup all game and as a result had only CS friends, not allies, because Greece was in the game dumping 50 quadrillion gold on them all.
You should play with only the friendly civs (portugal, venice, arabia, morocco, byzantium, brazil, netherlands)
Workshops before universities seems like a mistake to me.
How many social policies did you have at the end?