That IS one of the theories. Dozens of species of (mostly) large mammals went extinct in the Americas in a very brief period right after the end of the last ice age. This is the period when one of the theories has humans first entering this hemisphere.
The theory has become somewhat un-PC recently, as it requires pinning the blame for one of the greatest extinctions of all time on the ancestors of today's native Americans. Can't have that.
There are other theories for the mass extinction, but it is a remarkable chronological coincidence if something else caused it.
Certainly ver similar extinctions occurred in New Zealand, Madagascar and elsewhere. But the Americas are a very large place and I personally find it difficult to envision a massive enough population of hunters to cause this.
I also have always found it improbable that a huge hunting group killed off the big animals. I say it was disease. These animals were isolated in the icy cold. Then it got warm and other animals from further south moved into previously glaciated North America bringing their diseases with them. Kind of like white man and measles.