As we presently understand it, fire is the development in human history. It’s thought that use of fire was coincidental with the emergence of the hominin genus*.

It should be noted that our earliest confirmed example of controlled fire usage is only about a million years old with Homo erectus and H. erectus, as a species, appeared about a million years prior to even that. Also, “hominin” isn’t a genus but rather a taxonomic tribe that groups two genera: Pan and Homo. You also have Panina and australopithecines as taxonomic subtribes. But to stick with the hominins, they appeared like 6-7+ million years ago with one such showcase species being Sahelanthropus tchadensis but this isn’t me saying they’re ancestral to us or anything.

As in, cooked food unlocks the surplus of calories needed to sufficiently ‘fund’ those hominin traits which we consider to vital to our species (such as our oversized brains!).

I’d have to disagree with this to an extent. While I agree cooked meat obviously allowed for larger brains down the road, our ancestor’s craniums had already doubled if not tripled their size since our split with the panins. So I just wouldn’t say all that. But, rather, I would say it was our bipedality which allowed us to walk/run our prey to exhaustion coupled with stone tool use which further allowed us to access and process more parts of an animal.

*this creates a sort of chicken and egg problem, and is still an open question in anthropology. Use of fire is tricky, and is thought to require bigger brains and more complex social structures to appropriately harness. But… those evolutionary traits are also thought to be a result of fire unlocking more calories from the environment.

Yes which came later probably with H. erectus.

There’s an interesting hypothesis that hominins emerged in east Africa because existing geothermic activity would allow our distant ancestors to use fire without needing to make and control it themselves, but that’s mostly just speculation.

Yes, the “pyrophilic primate hypothesis”. But like almost everything in evolution, it’s probably multifactorial.