Evidence from the Boxgrove (England) excavations show that hominids
were capable of killing large animals already 500000 years ago.
There are other ways to hunt than running up a prey and hit it
with a stick. Probably animals were not so afraid of people in those
times.
I have a theory about expansion waves. When early humans first
learned to hunt, the animals where not more afraid of them than of
chimpanzees, so they were easy to hunt. After some time only the ones
with the trait to flee from man would remain. So man had to move to
new
hunting areas, where animals were still not so scared. But also some
people remained and after some time developed better hunting
techniques.
So they could get the game that was a little harder to hunt. And after
some hundreds of thousands of years it was time to move again, into
areas occupied by more "old fashioned" people. And so on.
The inventions and environmental pressure has in this way been highest
in the kernel area, Africa, and new "versions" of Homo has spread from
there
in the need for game that was easy enough to get.

- Hans