It is highly unlikely the native population the US entirely “disappeared” without native blood persisting in the white population. Likewise, many of the tribes have significant amounts, or in the case of the Cherokee, majority, European ancestry. That is why Italians can “pass” for Native American, the typical “Native American” might be far more European than Native American genetically. Assuming a generation time of 25 years, a person born in 1975 would have two ancestors born in 1950, 8 in 1900 (great-grandparents), 128 in 1800, and 2048 in 1700, assuming no in-breeding. Of all the ancestors, it is unlikely that every one of them married a 100% white person.

Conversely, assuming that a native woman married a white man, if they only bred at replacement level, they would have 2 children born in 1725, 16 descendants in 1800, and 2048 in 1975. If, instead, their descendants increased a the rate of the world average (which is still an underestimation) they would have about 20,000 descendants born in 1975.