What original natives? You mean the Asians that migrated down to what's now Canada and the US?
In the end it's a definition of how far back you want to look to define "original natives". And the further back you go the more inexact are the "facts". Do we all come from this one place in Africa in the end? Are we 100% Homo sapiens Or How much Neanderthal is in us? Does it depend on which migration wave our ancestors were part of?
Meaning by extension of your logic if I choose the right cutoff Europe is African actually so the Atomic bomb was invented by an African!
Personally I think that the cutoff should be somewhere around second or third generation immigrants. Specifics can depend on how much integration with existing local culture happens or how much individual silo groups cling to their country of origin. And then there's of course the "eradication of previous inhabitants" that sometimes happened. The majority population of the US has roots in Europe, yes. But US culture" is definitely distinct enough now to stand on its own.