Why subscribe to the endurance running hypothesis, though? There are no contemporary examples of humans hunting that way, and hominids were already making tools by the time they had developed to subsist on meat. The endurance/persistence hypothesis doesn't even make sense without tools like spears, knives, or arrows, because humans don't kill their prey by biting into them. If they had access to primitive weaponry, why would they waste energy running when they could instead ambush? Even other species like chimps and dolphins, that can't chuck spears, hunt by surrounding their prey. The only reason the hypothesis is even a thing is because people find it confusing that we sweat so much.

If anything, the persistence running hypothesis in some way discredits the idea that hominids relied on rotten meat. If they could catch fresh prey, why eat spoiled meat? Yet our stomach acid has a very low pH, more acidic than even that of cats.

What's more likely, in my opinion, is hominids began to supplement their diet by eating the leftover kills of larger predators as well as any rotting carcasses they may have encountered, and then developed hunting strategies around when they began developing tools. Even having sharp knives made of stone or volcanic glass would have been an obvious advantage in food procurement, and it wouldn't have taken millions of years to figure out that slashing an animal's throat in the right place would take it down quickly. No need for persistence running at all if a group can corner a mammoth or buffalo or lead it to a dead end.