You're surprised by this? Americans primarily came from Europe.
Culturally, Americans can be defined by the Constitution, the 'inalienable rights' as defined in the Constitution, and the fruits of that (relative) freedom. I would define an American anyone who is a citizen (as legally defined within the Constitution).
I suppose I don't really know what you're asking?
Ok, thank you for response. A few remarks. You say that "Americans primarily came from Europe" but there were no americans at that time. They were Irish, English, Jewish people etc. Culturally they remained who they were before. They only changed their place of residence.
More complicated question is how can you define American culture? Constitution is not enough in my opinion. My point of view is that America is "nation of nations" and there is no American culture at all.