1750 win here (turn 260 AD). 9 turns slower than Neuro, which I might try to beat at another time. I thought I easily had him after my Cristo went up, but then I realized I estimated the number of Social Policies I needed incorrectly (Didn't realize you need to unlock 30, not 25 policies!). Other note is that there were only 3 Culture CS in my game. That really sucked.
Anyway, my opening was very similar to everyone else here. Stonehenge->Great Library->Oracle is the main idea. I built a second city though, which is why I may have been slightly slower than Neuro. However, instead of taking Civil Service with my free tech I took Theology, and used my first few Great Scientists to bulb up to Acoustics. Meanwhile I researched up to Steel on the bottom which allowed me to upgrade my 2 starting warriors to Longswordsman + 1 Swordsman gifted from a CS, and started conquering my continent with 3 Longswordsman. Took over a good portion of my Continent when I decided to be lazy and said that was good enough, when I probably should've finished my continent off since there's no penalty for being in war, and on the plus side I would've spawned some more Great Generals for Golden Ages. My empire was largely fueled by buying out all the City States, after unlocking the 1st 3 in Patronage.
I didn't realize how powerful the Cristo Redentor trick was so I only started saving once I was relatively close to it. I might've shaved a few turns had I stopped after getting 4 in Patronage (I think the science boost is the last must have).
My policies went Tradition->33%Wonder Saving -> Patronage -> all Patronage except for the Happiness one -> Freedom. Took Order as my 5th tree, since I wanted the extra 5 hammers, because I thought I was going to be production locked instead of culture locked in the end. I was incorrect, and still had to wait like 5-10 turns after finishing the Sydney Opera House before I could start on the Utopia Project.
Anyway, my opening was very similar to everyone else here. Stonehenge->Great Library->Oracle is the main idea. I built a second city though, which is why I may have been slightly slower than Neuro. However, instead of taking Civil Service with my free tech I took Theology, and used my first few Great Scientists to bulb up to Acoustics. Meanwhile I researched up to Steel on the bottom which allowed me to upgrade my 2 starting warriors to Longswordsman + 1 Swordsman gifted from a CS, and started conquering my continent with 3 Longswordsman. Took over a good portion of my Continent when I decided to be lazy and said that was good enough, when I probably should've finished my continent off since there's no penalty for being in war, and on the plus side I would've spawned some more Great Generals for Golden Ages. My empire was largely fueled by buying out all the City States, after unlocking the 1st 3 in Patronage.
I didn't realize how powerful the Cristo Redentor trick was so I only started saving once I was relatively close to it. I might've shaved a few turns had I stopped after getting 4 in Patronage (I think the science boost is the last must have).
My policies went Tradition->33%Wonder Saving -> Patronage -> all Patronage except for the Happiness one -> Freedom. Took Order as my 5th tree, since I wanted the extra 5 hammers, because I thought I was going to be production locked instead of culture locked in the end. I was incorrect, and still had to wait like 5-10 turns after finishing the Sydney Opera House before I could start on the Utopia Project.

it gives me a black screen. Is there an easy way to do this?



You need to play as Arabia for it to be eligible for the gauntlet. No big deal for this one, and you're not the first to do it. But always good to check the required settings before you start a specific challenge. Other than that, as you found 3 cities is a big increase to total culture required, particularly if the other two don't build everything cultural.