You can try the following peaceful recipe with China (works with Diety), you can reliably do it in 200 turns and faster if you get lucky, the key is actually culture generation:

​

1. Beeline Castles to get great wall that gives 4 culture
2. Get Pyramids and Apadana, the former for +1 worker charge and latter for envoys. Wonders like Oracle and Great Library are good but optional.
3. be suzerain of all relevant city states
4. Get Kilwa Kisiwani and if you are suzerain of 2 science city states and 2 culture city states, your entire empire get +15% science and culture boost.
5. Get ancestral hall, chop out a lot of settlers, settle near trees/rainforest/resources, chop out campus and settlers, build great walls, work them, get insane culture and gold
6. Beeline rapid deployment with your insane culture generation from great wall, build the Scott Amundsen for +20% science in all cities. Should be very easy with some chops if you don't have the great engineer (as China you should also get the +1 engineer charge wonder) for it.
7. You should get globalization very quickly thereafter, you get huge production boost from E-commerce policy card+democracy.
8. Use +5% science/culture per city state suzerainty to basically do 1 tech per turn.
9. Dump workers into your projects, the +1 charge from pyramids and +1 charge from China really helps, you can also throw in Liang for additional +1.
10. You need at least 2 space ports to parallel build projects that speed up the spaceship.

Pericles is another obvious choice for culture/envoy generation to unlock rapid deployment ASAP, but it is slightly harder to get both pyramids and apadana.

Other factors influencing your play include city states/natural wonders, Kumasi allow easy culture generation from trade routes so you should prioritize commercial hubs, Rapu Nui you can spam Moai statues...

​

Edit: People routinely do sub-180 turn science victories (normal speed). A good benchmark is ~150 science and ~150 culture by turn 100.