Which "Age of Man" (Golden, Silver, Bronze, Heroic or Iron) does the story of Heracles/Hercules take place during?

Actually, Hercules came into existences during the Bronze Age............... Also, you need to remember that Hercules also started out as an Egyptian-demi god long before he became a Greek demi god...............

Bronze age would be my guess.

The Heroic Age is the one age that does not correspond with any metal. It is also the only age that improves upon the age it follows. It was the heroes of this Age who fought at Thebes and Troy. This race of humans died and went to Elysium. Before Homer's Trojan War, Heracles had made an expedition to Troy and sacked it.

Heroic Age

Great question! Let's see. He predates the Helenic times which were 3,000 BCE, or 5,000 plus years ago. Let's say between 5,000 and 5,500 years. I'd have to go with Bronze.