Flint spear
The very first weapon in history. The flint spear was simple yet very effective in hunting and sometimes battle. If a demigod is without any real weapons making a flint spear would be for the best.

It is made from a long stick or branch which has been found or carved straight, which forms the shaft. Then a rock is chipped into a triangle shape with a sharpe edge, which forms the spear tip. The tip of the shaft is then given a thin crevease where the tip goes in. Leather or string is then rapped around the spear tip.

After that you have a primitive but still very useful weapon.