Approximately when did Hercules live?
First, it is important to understand that Hercules (also called Herakles or Heracles) was mythical figure. He was said to be the son of Zeus (the most powerful of the Greek gods, known in Rome as Jupiter) and a Greek woman named Alcmene.
Ancient Greece is considered to have run from about 1100 BCE to 146 CE when the Romans conquered. The legend of Hercules continued in Rome at least until paganism was officially outlawed in 380 CE.
It is often true that legends or myths are inspired by real people. However, there is no real evidence of an actual Hercules-type person. There are some who say there was a great warrior who inspired the myth, but that the Romans destroyed all records of his existence.