https://www.livescience.com/woolly-mammoths-in-north-america...
I think it's more the case of if they didn't have the ability to create a balance. Things like the creation of the Amazon rainforest and the domestication of corn, potatoes, tomatoes, quinoa, llamas, etc. were because Native Americans figured out how to do those things. It's likely though that the first Native Americans just didn't know that stuff yet and accidentally ate all the mammoths or whatever because they didn't yet have a tradition of "only eat the mammoths when the third moon rises after Orion returns" or whatever. Those kinds of cultural traditions are social technologies, and they enable ways of life that would otherwise collapse in a few decades.
In the Pacific, Hawaiians and others had seemingly useless taboos like "women can't eat bananas" but following the taboo rules sustained a huge population (estimates for Hawaii vary, but it was at least a significant fraction of the current population without international shipping!).
In the Amazon, manioc is a great staple crop… as long as you serve it exactly right so you don't slowly poison yourself. They figured that out, but I'm sure there were many generations that got it wrong before they got it right.
So I don't think the framing should be "plains Indians didn't know how to kill off the buffalo." Rather a) plains Indians didn't have horses pre-European contact, so that whole way of life didn't exist until modernity and b) balancing with nature is a learned cultural achievement.
Kind of a ridiculous myth when you consider the diversity of life uniquely adapted to the various micro environments of the amazon rainforest. It would be multi-million-year terraforming project.
Buffalo on the other hand reach sexual maturity at 2-3 years, there were many more of them. They replaced their populations faster.
The first humans in North America didn't extinct buffalo because they couldn't, they would have had to have much more population and civilization progress before that became a risk.
I suppose in the absence of any historical record you can make up whatever story you like, but the self flagellation that comes with it is so weird.