“thousands of years ago” isn’t the kind of resolution I was interested-in.
IF the genetic-drift-rate ( or whatever it’s called ) of the critters is known,
THEN it should be possible to identify when they came here from Asia, through cladistics.
That may be another torpedo-hit in the “there is no evidence the Indigenous people were in the Americas significantly before the interglacial began” prejudice.
( there is already plenty of evidence that they were here, but when dealing with ideology-addiction/prejudice, you have to keep nailing the damn coffin closed, until the prejudice stays dead )
Head lice hitched a ride on humans to the Americas at least twice (www.sciencenews.org)