Thank you Skinney! Any Idea where I could find reference to this in case we would be confronted at the range for example?
Yes, present your tax stamp.
Sadly, I don't think it's going to be that easy. The laws tell you more about what you CAN'T do. The laws would be thousands of pages long trying to cover all of the "can do's."
If you read the Federal laws, and I suggest you do, no one under the age of 21 may buy from a dealer and no one under 18 may buy from an individual or possess under a trust. The laws also define a "transfer." Shooting at a range and letting someone else shoot while you're right there isn't a transfer. But "loaning" it would be. So don't let it leave your control.
State laws can vary so you should read up on those.
But if you're looking for a law that says you can, you're probably not going to find one.
There would be much more to be concerned about than just mentoring your kid with your suppressor then. Such as, how can the state even allow a mentor tag, that will allow a 10 year old (8 years under the legal age to own) to be in possession of a Firearm that is not registered to them, and still be allowed to harvest a big game animal with it. Same thing at the range, if your concerned about a RO confronting you about your legally obtained suppressor, he'll probably be complaining about you letting your kid shoot a firearm (rifle/handgun) that isn't his as well.
If the firearm whether it be a Rifle, Handgun or Suppressor is legally registered to you, bring the proper documents, and always be present with the shooter. If it makes you feel more comfortable I have multiple videos out hunting, shooting with my kids, all who aren't legally of age to "own" a suppressor or Rifle, But I am mentoring them, allowing them to shoot, and hunt with my legal possessions.