Honest answer, usually animal sinew, or certain grasses could be used as well. The nice thing with string, once it was figured out was you could make as much as you could, and make it as long as you wanted.

How do you think they got the stone on the end of a stick

For a long time, they didn’t.

Hand stone tools predate everything except sharpened sticks as spears.

Without the Olduvai tools, we have no civilization.