The outer rim 4 pop cities never go below +1 happy because of Estadio. The bigger cities, and all various 7 pop ones scattered throughout the map for IZ radius are +1 from amenities usually, or entertainment radii. The majority of cities in the middle are around 10-13 pop, and eat up the base amenity distribution, 2 extra each from being aztec, but even without aztec it's still enough to never go below content. Biggest boost is Estadio though. No reason you can't build it first if you're snowballing hardcore.
Funny you should ask this because I did a Rome game awhile back, specifically to test this.
https://forums.civfanatics.com/threads/40k-gpt-64-gb-ram-test.615704/#post-14757437
The thing that takes the most time to calculate are actually the trade route pathing and yields instead of the cities. I did this test when I upgraded GTX 1080 and also randomly bought 64 GB of ram overkill. Oh someone asked for processor in other thread, I'm still on ryzen 5 1600x, waiting for a good deal. Before upgrading, I woulda ended the game much earlier, or went for high score or something and eventually quit out of boredom.
Anyways, the game never goes much past 5 GB of ram usage, even on 700 trade routes, which is around where this game ended. The Rome game had slightly less, but I timed it using my phone stopwatch. Around 400 trade routes, the turns were taking around 230 seconds. At the end around 700 trade routes, each turn took almost 500 (so it's not linear, rate decreases even more).
8-9 minutes is unbearable if you're sitting there waiting, even the 230 seconds was pretty bad. It increased my cigarette consumption rate, so In the Rome game eventually I loaded up two long movies I'd never gotten around to watching (Cloud Atlas and The Grey), pausing the movie while I took my turn. For the Aztec game I watched 9 episodes of Better call Saul. Basically did absolutely nothing all day one Sunday.