Depends on the state. In general, it's illegal for anyone to operate a weapon until the age of 18 (with exception if you are 13 and supervised) but most jurisdictions place the blame on the parents, and they would get in trouble. Notable though, having access to something is often argued in court about "access" means.

There was one case of a court ruling that a parent was neglectful for allowing access to a gun, but the gun was unloaded and locked in a safe. Since the kid was able to crack the code to the safe, and figured out how to load the gun. Don't remember what state that was. Probably New York or California.