Even if you only try to explain the changes in brain, body, and behavior since we last shared a common ancestor with the chimpanzees, many things appear potentially important. Worse yet, there are some seductively attractive processes that might have sufficed, given enough time, to do the job of enlarging the brain fourfold. Good old compound interest reasoning, sheer intelligence bootstrapping itself, little by little. Physicists who make grandiloquent statements regarding life in the universe are particularly prone to such one-sentence summaries. They are brief intermissions in the grind of ordinary times when interesting things happen.
Evolutionary explanations involve a lot of such messy details, threatening the grand generalities.
Since the unique history is important, piecemeal answers are inevitable. We keep wishing for a sturdy framework on which to hang the pieces. But they do hang together in a way that helps explain how the more elegant human abilities might have emerged. Abrupt climate change makes versatility, often a virtue, a necessity. There were many abrupt shifts during the last 2.5 million years of fluctuating climate known as the Ice Ages, quite in addition to the slow advance and retreat of the continental ice sheets.