If you break pizza down to its simplest form - flatbread and toppings - it’s been around for a very long time.
But tomatoes didn’t exist anywhere outside of two isolated continents until the turn of the 16th century
Tomatoes had to be brought from South America to Europe. After that it was quick.
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.
The modern version of a pizza is sometimes said to have been invented in the late 1800s, since that is when the first “proper” recipe is from. But there are a few key points that might inform your question and other answers:
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Flat bread baked with toppings already on it has been a thing for several thousand years across the world.
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Among which was a type of street food referred to as pizza in Italy before the Tomato arrived in europe
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Tomato is from the Americas, it wasn’t known and didn’t exist in europe until the mid 1500s.
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On its own a fresh tomato is not very nurishing compared with other common fruits and vegetables, and since toxic versions exisited, it was mostly used as table decoration in places like Italy for a while.
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The first mention of tomatoes as an ingredient in an Italian cookbook is from 1692. And it wasn’t widely adopted as a staple food until the 1700s.
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There are descriptions from the mid 1800s talking about the wide variety of pizza toppings, as it was already an established food by that point.
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Just read this article