This is more of an archaeology question since bows are prehistoric. The oldest bow found is the 'Holmegaard bow' found in a bog in Denmark, dated from 7500BC. This is the earliest proof of a bow, but not the first. It just happened to survive because it was preserved in a bog. Earlier bows would have just rotted away, and the only evidence left behind are stone arrow points which could be from arrows, javelins, darts etc so it starts to become guesswork from there.
Hiya, you'll find more info in the FAQ