I was about 5 when my dad started taking me hunting with him. I was allowed to carry my toy gun but only as long as I handled it safely. I was 9 before I got a BB gun. I was not allowed to carry a loaded weapon until the age of 12 and passed hunter safety.
IMO, even under supervision, anything less than 12 is too young to be given a loaded firearm more powerful than a BB gun. But that is the way I was raised.