The only thing we know Paleolithic people ate a lot of is meat.
Paleolithic archaeological sites are full of marrow-scraped bones and the stone tools used to kill and butcher. Paleolithic teeth have little of the damage associated with eating grit from ground grains. We have such remarkable discoveries as a building made entirely of mammoth skulls.
The Hadza are a modern people, and modern hunter-gatherers have been pushed to the fringes. Early English and French explorers documented the diets of the North American people they encountered: they ate a lot of meat, growing the Three Sisters as a supplement to a diet heavy in game and fish.
It was the Neolithic in which population pressure forced people to start eating grain, and eventually growing it. They immediately became shorter and their teeth started falling out.