For a normal size map, especially if you cut city states ratio down to 1:1, then I'd suggest playing one of the civs with happiness bonuses.
The biggest one of these is Indonesia on Tiny Islands map (4 cities, every city on its own land mass.)
Tradition, at least one religious follower belief with happiness, Top right of Exploration (happiness from naval buildings) as filler, Massive trades of luxury for a luxury.
If you've gone specialist driven, you might be able to get it quicker with Freedom (level 2 tenet with happiness from specialists), otherwise its Order.
If you want to put that happiness to work (as opposed to only having it for the achievement and Golden Ages), then you can also dip into Aesthetics for a policy that gives you culture from happiness.