I've been reading Wengrow and Graeber's "The Dawn of Everything", and one of the main points they've made so far is that once modern humans became recognizable as such, we were doing all the human-type things we do now: thinking about our place in the world, debating different ways to live and their pros and cons, and so forth.
We tend to think of prehistoric humans as being stupid cavemen, but I suspect we'd find them to basically the same as us, just with a different context and level of knowledge about some things - but also far greater understanding of other things.
I wish there was any way to know when language was developed in (proto?) humans. Our complex grammar is pretty unique in the animal kingdom, and it's clearly linked to our cognition. You can get pretty far with mere vocabulary (just look at the great apes), but once you get into the world of words modifying words and recombining into sentences, you have an absolute explosion of expressible ideas.
When did that happen? IMO, it's pretty clear the Chompsky school is at least partially correct in that we have biological hardware for grammatical language. So we've probably had language as long as we've been homo sapiens. Neanderthals probably spoke, too. But what about Homo Erectus? Australopithecus?
> ...and it's clearly linked to our cognition.
People with global aphasia can still do arithmetic, follow causal reasoning, play chess, pass theory-of-mind tasks, etc. During non-linguistic reasoning, math, music and executive tasks, neuroimaging has revealed that the language centers in the brain are pretty darn quiet.
So the link, and the causal direction if any, is not really known.
My entirely layman and unsupported conspiracy theory about language is that early hominids likely developed complex sign language and some primitive forms of writing now long lost to time, but vocal language only came with the necessary biology.