Its hard to say much about pre-history, but we do know that people could remove their facial hair and probably did in pre-history. Obviously this probably varied across cultures, but removing facial hair is fairly common everywhere in the world. There are plenty of cultural variations in support of beards or against beards, but rarely are long flowing beards seen positively in human society except on older men as a sign of age and wisdom. Most times younger men in societies that are pro-beard keep them trimmed and neat as a way to show they are adult men, but not ancient. Having a large beard serves little utilitarian purpose and can be a liability just like long head hair. It can be grabbed by an enemy in a fight, get caught in things, gets dirty and tangles, and doesn't keep you much warmer than a shorter beard.

Early men probably plucked the hairs out by hand or with a clam-shell or scraped them off with a sharp stone or sharks tooth. We observed these in cultures that did not have access to metallic razors like early North American Native Americans, and there is other evidence in cave drawings. The total removal of a beard down to the skin helps keep your face cleaner, makes eating easier, and discourages bugs like fleas and ticks. I myself knapped an obsidian razor and shaved myself with it in an experimental Anthropology class as an undergraduate. It works quite well but takes some practice. Many people around the world still pluck hairs as well.

Even assuming they did not shave it down to the skin, which is probably rarer due to the damage dry shaving could do to your skin, it is doubtful they grew long flowing beards. Hair is easy enough to crop short with a sharp stone, or it can be torn by hand, bitten, and even burned shorter. The hair can then (assuming it was not burned) be used for other things.