I am pretty sure that modern archeology agrees with you in at least some ways (know an archeologist, not an archeologist). I don’t have any specific evidence for mammoth trapping but there are these really interesting stone funnel traps that were used to trap gazelle herds …blogspot.com/…/ancient-gazelle-killing-zones.htm…
Also consider how long humans have walked the earth as hunter gatherers. Agriculture goes back to around 10.000 BCE. The entirety of time between 300.000 BCE and 10.000 BCE was likely (mostly) spent as hunter gatherers. Imagine in how many ways local roles and culture could have differed in that time!