I tried to get a fast cultural victory with Mughals now, and it wasn't faster than the same game with France.
Here's some info on the Mughals run:
- unlocked natural history on turn 6 (boo!), and immediately bought 3 explorers (yay)
- bought additional ones on turn 7 and 10, then 15, and later with hegemony (see below)
- natural history revealed 8 total artifacts on the map
- of these, I got 6
- I also got 3 from natural wonders, and 1 from city states.
- I got one from events/overbuilding
- that's the state at turn 35, when I unlocked hegemony: 11 artifacts in my museums.
- at turn 40, I had enough. I actually hardly needed hegemony, as I got 4 more from overbuilding in these turns.
- my production was bad: it would have taken till turn 55 to build the world's fair. I unlocked the civic to buy it in turn 54.
- it was the fastest victory for Mughals, I only had 170 economic points in that case. Although, if I hadn't invested so much in museums and explorers, I would have had 30-50 more, but still not enough for a quicker victory.
With France, I unlocked hegemony in turn 27 (I believe, I forgot to take a note), and had all needed artifacts by turn 36, and could have built the world's fair by turn 48.
I know the comparison isn't bulletproof. While the map (and thus artifacts on the map) and previous game was the same, there's a lot of luck involved with how it plays out with the AI. And the overbuilding/events artifacts seem very random. It's kind of funny that I got 4 "free" artifacts between turns 35 and 40 with the Mughals, but only 1 before turn 35. With France, I also got the free ones from explorer research (which I believe you get if you are the first to unlock natural history and hegemony, but I'm not sure), which I didn't get for Mughals.