EDIT 2: 3 cities is kind of low. You're going to have trouble breaking out because your productive capacity isn't high. If you're planning to war, the only redeeming quality is the forests around your capital. Settling on that Incan city of Tiwanku spot is critical on this map.
If i play out the save I have on that I think the capital + the other two contributing a little will be ok to war with. I didn't expect to get hemmed in so quickly since i don't play immortal normally. If i had expected war this early I would not be researching priesthood -> literature. Probably would have gone down horseback riding and construction. Anyway epic speed is too much for me, so I'll probably won't pursue it.
I am keeping up in tech on immortal due to the monster capital. Yes it starts out food poor, but its got 4 flood plains, a gold, and decent production once you get worker turns into it. I probably should have chopped out more settlers + workers then I would have a couple more good whip cities and could roll someone over.
I think you are right that if you can get a settler out quickly to block Tiwanku which almost always seems to be in this spot:
My question to you is how you did this? I have restarted and run the game a few times to see what happens and they settle the city on turn 29-30. How did you build and get a settler to the site before the AI, which starts with a worker and two corn tiles?
Original save attached: