Thats way I teach it alright. Many animals make and use tools. Cooking is just one tool. Each organism (species) has those attributes that makes it fit and competitive in the world.

Eagles have amazing eyesight, strong talons and beak, and strong wings to acquire its prey. Cheetahs have speed, claws, and enlarged incisors to grapple and hold its prey. All organisms have their adaptive attributes and characteristics that allows them remain their evolutionary fitness.

Humans are no different. Back when humans were still becoming, they as a spevie
species were smaller thn their prey (mammoth, mastodon, etc) and much slower and weaker than the things that preyed upon him (cave bear, smilodon, etc.). Therefore they couldnt outrun, theycouldnt out wrestle, they couldnt out fight.

What they adapted was a complex society and language ability. This allowed insipient humans to express abstract ideas and work in complex societal arrangements. As these skills developed, they were accompanied by the ability to use that abstract thought process to modify things in their environment (tools). As those that were better at communications and abstraction lived long enough to propagate, their improved abilities were passed onto prodigy. Each generation became better adapted and more evolutionary fit. It took hundreds of thousands of years for these changes to manifest in the species we know today as Homo sapien sapien.

It did not hurt that our pre-human ancestors had opposable thumbs and passed them on. It gave us the ability to better control objects for manipulation and alteration. The more we used our communications skills, abstract thought skills, and manipulation skills, the more those crnters of thecbrain grew. Not because using them makes them grow, but because those with were better adapted and successfully passed their traits on to their progeny.

This is the short answer but you get the idea.