To quote Vertigo: Although some might say, you cannot ever teach them young enough, I beg to differ. I believe letting them handle and shoot a firearm shouldn't be for any under 10 year olds.
You prefaced that you are not a gun owner; that is obvious. Like many here, I have been handling firearms since I was literally 3 years old, and shooting small caliber centerfire handguns since I was around 5 years old. All with supervision, strict supervision. As with anything, the person learning must be mature enough and supervised enough to handle the situation accordingly. You might as well say no one should drive until they are 25 years old. Oh, by the way, I have tought dozens to shoot the M16A2 service rifle, and between myself and all of my students, no one under my supervision ever had a negligent discharge. That is because I live and breathe safety, and always will.
My teaching included this restriction: I didn't own a BB gun until I was 15 years old, and had to purchase it myself. I already owned 2 .22 rifles and a 6mm Rem. deer rifle by that point. My father refused to buy me a BB gun because he didn't want me EVER thinking that a firearm could be a toy. Something I carry to this day.
Parents, teach your children responsibly about firearms, and you have to be the judge of when they are old enough to use them properly.