There is very little evidence for the idea of persistence hunting ever beeing a thing.

Despite the idea’s foothold in popular culture, however, there is no hard evidence that ancient humans were persistence hunters, much less that persistence hunting shaped evolutionary traits. In fact, what evidence there is doesn’t support the notion that early humans acquired their meaty meals through feats of running endurance; it flatly contradicts it.

https://undark.org/2019/10/03/persistent-myth-persistence-hunting/