I don't think there's any evidence of that. Megafauna aren't that easy, and there's no general evidence of overhunting all the animals. People weren't going hungry because medium-sized animals were still around, and there are so many more of them!
Agriculture, at first, simply made life easier. You didn't have to be nomadic always looking for more food, you could just stay in one place. Your food was right there. It was awesome.
The problem was, it was so insanely successful -- you were having so many more children because of all the food -- populations shot up and suddenly there wasn't enough food anymore when you had a bad year.
So it's actually the opposite of what you're describing -- from what I understand, famine wasn't really a thing until agriculture caused populations to increase massively.
Agriculture, at first, simply made life easier. You didn't have to be nomadic always looking for more food, you could just stay in one place. Your food was right there. It was awesome.
The problem was, it was so insanely successful -- you were having so many more children because of all the food -- populations shot up and suddenly there wasn't enough food anymore when you had a bad year.
So it's actually the opposite of what you're describing -- from what I understand, famine wasn't really a thing until agriculture caused populations to increase massively.