Depending on which Native Americans we're taking about, some of them drove entire herds of bison over cliffs. Our European ancestors hunted the mastodon to extinction, I think? In Australia and New Zealand a bunch of reptiles and the moa birds were wiped out by humans.

I don't think most humans are ever thinking about genocide exactly (probably some are/were), but that they're focused on feeding and defending their communities and not considering the balance of the ecosystem.