The word you’re looking for is ethnogenisis: https://en.wikipedia.org/wiki/Ethnogenesis. There is no “American” ethnicity, though “white people” might come close to being considered a synthetic ethnicity resulting from the immigration restriction and birth rate boom from 1921-1965.

But even that is too broad. It might be more accurate to get even more granular. For example, you might identify someone like Tim Walz as belonging to a synthetic Scandinavian-Midwestern ethnicity: although he has no actual Scandinavian ancestry, he grew up in Minnesota in what’s a recognizably distinct ethnocultural subgroup.

A far more useful analogy might be that “American” is a college football team.