For the purpose of a spectator event it's whenever the Romans starting doing it. As an event where the participants began to get paid is anyone's guess. As a sport with carefully thought out and enforced rules it's the mark of the Queensbury rules.
1892, then...based on the fact this was the year when they began to be used in heavyweight championship fights.
Dawn of time Egyptians and Mesopotamians had it but it probably was more ceremonial. Ancient Greeks might have invented competitive sports, including boxing.
