Gee, how far back does it have to go to be authentic? Tomatoes weren’t in Italy until after Columbus brought them (of course after 1300), and didn’t catch on until well after the later date mentioned of 1700, so there goes all of Italy’s most famous dishes.
Hamburgers are American food. Not Native American food, but American. Next you’re going to tell me baguettes are Middle Eastern food because grain was domesticated there, or that camel meat is Native American food because they evolved in America before crossing the land bridge in pre-human times.