figure out the turn where it first appears in South America
Am I looking for the first sign of any influence in SA, or the first in roughly the Inca/Aztek regions?
I find very early influence in Brazil. Right in the turn that Catholicism is founded, and in Suriname (49°22 W/5°29 N).
The attached savegame is a close reproduction to what went down in my game. If you get the same random numbers like I do (I don't disable the RNG, but I am not 100% sure whether the RNG seed gets saved too), Catholicism is about to be founded right when you click for the next turn, and Catholic influence in Suriname jumps from 0 to 1 at exactly that same time. Within the next few dozen turns, land in Columbia and Brazil is all converting from 0 to 1 as well, while the greater Peru region is, at first, not yet following that trend.
Perhaps it has something to do with proximity? The Suriname spot is suspiciusly almost exactly 14 tiles SE of Lisboa, although I doubt it has something to do with it.
This here was my older post about Catholicism spreading to the Maya extremely early, in a 1.15 game. I could still dig out all the French savegames, but not test them unless I convert back to the old version. At that time I was doing a similar stunt like I was attempting now, only with Roman->France instead of Roman->Portugal, and the Catholic shrine just happened to be in Nîmes (Marseilles).
Lisbon is very strange as it is the portugese core, roman don't build there or carthagian.
Olympian-Roman Lisbon (Felicitas Julia) was turning into Orthodoxy just the right moment. So that there were more orthodox cities in non-orthodox civs than there were in (christian) Egypt. Which was the base for Catholicism. It was a neat, lucky coincidence.
Portugal is the only non-Polynese nation that can realistically build the Moai Statues. Well, I mean, the Romans can build them before they switch to Christianity. Which is what I did here, with the clear intent of switching to Portugal. You might say it is cheating, although I'm doing it to offset the Emperor difficulty level: On that diff level, my starting civ will be abysmally bad in every respect, but they CAN lay the foundation for the actual playing civ that I'm going to switch to. I think of it as a decent starting boost that brings my player-civ to a competing level.
With the Azores-Moai statues and Lisboa as the shrine city... okay, it's a really unfair boost, alright. My Portugal game is cornering the UHVs really early.