Fair enough! That's where early internal trade routes can help. A trade route to the campus/gov plaza city is worth 3 food and 2 production. Civs like Persia and Cree can boost that even further. That speeds up the first CH quite a bit. The bigger problem I find after a few more games is low culture per turn because markets often get priority over monuments. In my Simon Bolivar game, I had 3 theatre squares but also 3x3 envoys in cultural city states and enough gold per turn to straight up buy amphi theatres. Pingala in that tall forest fire city was another 13 culture which I wouldn't normally get. So I think this strategy might work best with civs who can generate a bit more culture with tile improvements for example Persia, Mapuche etc. Or it really is map dependant and you need those cultural CSs. I'll experiment a bit more.