Ancient Native Americans came face to face with sabertooth cats

I don’t think you can squarely rest their disappearance on man. I think their populations would have already had to have been effected by climate change and on a natural death spiral. Humans probably helped things along in that respect, but if their populations were as healthy as say bison, elk,moose (mooses? meece?), or brown bears (not quite mega-fauna, but not tiny either) there’s no way man could have hunted them all down. Native Americans didn’t kill what they didn’t use, and the Americas are so vast with wilderness it would have been a challenge to kill them all even if it was their goal.

Also - where can I find what the range of sabertooth cats were? My ancestors are from the Great Lakes region (Pottawatomie). It would be neat to think they were cat hunters.