The Indians came from Mongolia and Siberia mostly. They probably were driven out by other peoples or by starvation, as nobody moves if they don't have to. As for the Pilgrims, to call them illegal aliens is nuts. I suppose if there had been one oriental who crossed over to Alaska and lived in the Americas and claimed the whole area for himself, then liberals would say that our ancestors took his land away from him. The usual argument runs that Indians believed that no one owned the land so the European had no right to the land since the Indians already owned it and that was the reason that they fought us for 300 years until Sheridan and Sherman put an end to it.
As for USDA, you can see that they are overstaffed and overfunded.