I had read as a child that some of the western indian tribes would herd buffalo to a cliff and run them over it.
Head-Smashed-In Buffalo Jump is north of me in Alberta Canada, and the Madison Buffalo Jump is over the hump by Bozeman, MT... It was a common practice.
Folks forget that the horse was a very recent addition to Native culture in the Americas (and I wonder about the bow too) Without such things,(and even with them as the Jumps prove) it is easier, and far less risky to herd an animal over a cliff, or into a squeeze chute in order to dispatch it without risk - I think that such practices were naturally far more prevalent.
Every hunter (including man) is an opportunist, with risk necessarily lent more weight than anything else.
Or they could corner it/trap it in a ravine or narrow place and hurl boulders at it or dig a pit for it to fall into or lasso it.
Lots of options for hunting large game, even back then, if you use a little creativity and knowledge of the terrain.