It's highly likely, at the beginning, us lowly humans were scavengers. Fortunately we were reasonably smart scavengers that could make tools and the like to break open bones and skulls to get at the lovely fat and good protein in the marrow and brains.
The other animals that would like to eat us and who made the kill in the first place didn't have the smarts to access the skull and bones for the goodness inside.
2000 calories is about 220g of fat, which isn't that much, kind of like a big handful.
As we became better hunters and better scavengers for that matter, we would of had more and more of the kill to ourselves, and access to plenty of fat, of which we eventually learnt how to keep to consume later on.
So getting enough fat, wouldn't of been overly difficult most of time. And when it wasn't you'd use your own.
Edit: A bit of an after thought.. Another good question would be to flip it and ask, How did Grok get enough carbs? During Ice Age there would of been infrequent and very little edible plant matter around. Fat would of been the dietary staple.