Frankly I don't think 'white people' existed ten to twenty thousand years ago - and if they did they weren't living in Europe. Whoever was living in Europe back then wouldn't look much like the folks living there now whatever their skin color, any more than the folks living in East Asia back then look like the ones there now.

Immigration, conquest and population replacement, (genocide is perhaps to harsh a term since the original inhabitants were as often assimilated as killed by the newcomers) was a fact of life in the Old World, why should the New World be any different?

I am delighted to hear Native Americans are not threatened by the possibility of early migrations from places other than Siberia since there is not one good reason why they should be.