In this instance, it would be migration not immigration.

Perhaps the OP is implying that without previous population, the first peoples of the Americas were settlers, not colonizers or immigrants.

To extend this line of thinking - you are (possibly) not an immigrant only if you were born in Africa - our place of origin.

Even "origin" is a misnomer here. It's not clear if the neanderthals were wiped out, or simply assimilated. Many were already living in modern-day Europe.