If I recall correctly, there is fairly good evidence for Homo Erectus’ use of fire including the ability to make fire dating to 1.8 mil years ago. This is in Asia and Europe as well as the Middle East. Wouldn’t the lack of a major food source just prompt HE to move on to a better environment. The fact is that HE lived in many areas lacking elephants or mammoths. They adapted to other food sources quite well.
Note how more broad based food packages result in larger brains. Or do larger brains facilitate more broadly based food?