Actually, there's considerable evidence that early humans routinely engaged in mass slaughter - start a stampede, guide it toward the top of a cliff, and harvest the meat and other useful parts from the bottom. Far easier than trying to kill animals much larger and faster than you directly.
The downside is that you end up killing a LOT more animals than you can use, but the problems with that aren't going to be noticeable in any one person's lifetime - at least not until the species is almost extinct. And even if people eventually noticed the problem, and their own culpability, cultural inertia is likely to have kept things going anyway. Just as it did when the Easter Islanders cut down the last of the trees their society depended on, or when modern humans keep dumping CO2 into the atmosphere at an ever-increasing rate.