I'm joining in this in response to Denniz's request.
I'm still in the process of trying to fully understand the new mechanism, so ...
I can explain it
To get a brand new settled city to Legendary status in one turn (or in more if you don't quite have that 60 spy army yet), you have to have 1 Great Artist do their great work (+4000

on normal speed), spread the religion that you own to the city with a missionary (for the -40% espionage bonus), and give the city to an AI.
Then you have to run a lot of espionage "spread culture" missions. The rule of 72 says that you need to do 72/1.05 = 14.4 spread culture missions to double the culture. If you double 4000

4 times you end up at 64000

. A bit too far.
So, you get out a calculator and find that you need 52 successful spy missions to get the 1 Great Artist culture bomb up to Legendary.
Besides 3 great artists and 156 successful spy missions to achieve victory, you need

to fund the missions. With max bonuses by placing the Legendary city as close to the capital as possible (which is also great for spies walking back for another mission

), you can achieve a 5:1

to

ratio.
This screenshot (of an epic speed game) indicates a more exact ratio of 5.64 roughly.
You need 150,000

total to win a Culture Victory.
Subtract out the 3 culture bombs and you need 138,000

Divide by 5.64 and you need 24,468

minimum to fund the spread culture missions with max bonuses.
Now if you get a few Great Spies, each infiltration gives +3000

instantly.
With 3 Great Artists and 4-5 Great spies (Scotland yard +100%

works great in a fat bureau capital), and running 100% espionage slider for the 2nd half of the game, you can get quite the great finish date!
Just have to be aware that AI only take gift cities if they are within 9.5 tiles of one of their cities. Notice in the screenshot I had to gift Mansa a city in the desert so that the Legendary cities were within range for him to accept them.
If you count extra close, you will see Legendary City 3 is a bit farther than 9.5 tiles away and Mansa wasn't willing to take it at the end of the game. (10 tiles away doh! Diagonal counts as 1.5 tiles)
After I picked my jaw off the ground, I noticed and gave him York. He was then willing to take Legendary City 3 and let me win the game after an extremely brief war to reclaim my Legendary Cities.
Also have to take care if "no city razing"
isn't checked to let the newly settled Legendary gift city grow to 2 pop before giving it away or it will autoraze when you declare war on Mansa and take it back by force.
"City flipping after Conquest" will also let the city come back to you naturally after the 2nd revolt given enough time if you picked that game setting too.
Theoretically, you don't even need a Great Scientist to bulb Philosophy to get early Pacifism for 100% great people birth rate.
The Aesthetics tech unlocks the wonder Shwedagon Paya which lets you run Pacifism. Parthenon for +50% GPP rate is good to build too.
Theoretically, you don't need any Great Spies if your empire can generate the 25,000

with the slider.
Theoretically, you also don't need any Great Artists if you can get 2000

(Half a great artist) in each Legendary gift city naturally by building a fat wonder in each around 1500BC and playing a cultural leader like Zara Yaqob (+25%

stele/monument!)
The additional doubling required if you went 2000

in a wonder city instead of 4000

in a Great Artist bombed city only demands 14.4 more spy missions.
The price for the extra 2000

that the spies will pay is 354

with the -50% bonus and 637

with only -10% bonus (you want the 10% at least to get 84% chance of success). So if you are in a hurry, you can pay almost twice the espionage points for the first few dozen spread culture missions and only wait for the -50% bonus for the last 25 or 30 missions if you are in a hurry and have extra espionage points. The first doubling is relatively cheap to fund.
So ya, I agree that spy spam can beat regular culture hands down for speed if you are careful.
And Mansa doesn't put his stack of doom in one of your gift cities and you can't take it back by force because you built spies instead of an army.
So many 1300 AD to 1600 AD HOF culture victory dates to effortlessly eclipse now (not sure about quick speed yet)
