This isn’t true. When you look at modern hunter gatherers who don’t practice agriculture today, the bulk of the calories still come from plants they forage rather than meat.
The megafauna extinction was in the Americas. Human coexist with megafauna in Africa: elephant, giraffe, hippo, rhino.
Megafauna don't make much of diet of African hunter-gatherers cause they are a lot of work to hunt. They hunt smaller game. Gathering is much easier and safer.