Well, the tomatoes were in the new world, and all the domesticated cows, sheep and goats were on the other side of the atlantic, so that's a minor problem.
I guess you could use like a llama cheese? That might work. Then I'm sure the indigenous people of the Peruvian region had a flatbread of some sort, just about everyone does. Then they just need to harvest up some tomatoes.
So, yeah, they could've. You need to be looking in the Andes in South America though.