I think the most important thing is what you feel to be and what nation you feel to be connected with. If your family came to the US from Czechia and your culture is similar to the Czech culture (traditions, dishes, etc.), then there’s no point in going back to the past and forcibly trying to connect yourself with other cultures. You’re officially Czech.
The deeper you go to the past, the more ancestors, nations and cultures pop up.
All people descended from the same ancestors, after all.
I understand that you grew up in a country where every white person knows that their ass originally comes from Europe (or its surroundings) and you’re naturally curious about your genealogy.
To us Europeans (or any native people) it feels like our ancestors have been living here since the beginning of time and we don’t feel the need to research our past.
A 2nd generation Slovak could tell you “I’m 100% Slovak and I don’t care what you think!”
Only noble families remember their ancestors to whatever century. We yokels usually remember only our great-grandparents at most.