There is no such thing.
People don’t come here from other places and become American. They come here and make America a little bit like the places they came from.
I believe I am part Irish because I love George M. Cohan and John Ford and James Cagney. I believe I am part African-American because I love Louis Armstrong and Robert Johnson and Jimi Hendrix. I believe I am part Jewish because I love George Gershwin and Arthur Freed and Bob Dylan.
I don’t mean this figuratively — I mean it literally. Irish and African-American and Jewish blood runs in my veins because tributaries of those cultures have coursed through my heart, defined who I am.
“Foreign” influences aren’t assimilated into America — America is assimilated into foreign influences. American exceptionalism is a dubious concept on most levels but not on this one. There has never been a country like America in the history of the world.
You want to know what American culture really is — ask me tomorrow. We’re still working on it.