I’m well aware that grains were not originally part of our original diet, until we went agricultural.
But neither necessarily were proteins highly available, as it wasn’t always easy getting our hands on food that can move. :)
We ate a lot of roots, since roots don’t run very far very fast and we used a lot of plants in our diet. Plants don’t necessarily imply grains. Grasses, roots, fruits, whatever we could grab and found delicious, basically.
Except the times we resorted to cannibalism. Those weren’t good times, I reckon.
There is a great deal of argument over how effective early Man was at hunting, particularly larger animals.
One end of the spectrum is your notion, that animals provided a relatively small part of his diet.
The other end has the first men to arrive in America exterminating most of its megafauna within a few centuries of arrival. The Clovis extinction idea. To be fair, the current is running at present against this theory. Similar extinctions occurred more recently in New Zealand, Australia, Madagascar, etc.
My POV is that in every environment on earth that we know of historically Man was The apex predator. Pygmies regularly hunted and killed elephants and Eskimos hunted and killed polar bears without firearms. I suspect our prehistoric ancestors were fully as capable.