My oldest had a new BPS the day he was born((long story).
At about 4 he got a pellet gun.
At 6 he got a 10/22. He "took over" one of my .17hmr.
At 7 he got a cute little .410 single shot.
At 9 he passed hunters safety, so we started the search for a small frame 20 ga. Mossberg killed his swan that year(with a 22" barrel).
At 11 he mowed all summer, saved b day money, bought himself a AR.
He is 12 now. Just bought himself a .30-.30. Santa got him a .50 muzzy for Xmas. He will be "borrowing" dads 7mm-08 for big game this fall.
His 7 year old brother is on the same course, only his 10/22 had to be red so it wasn't like his older brother.
Point is this. I don't live where I can hand them a bb gun and let them run like I did as a kid. But I like to shoot guns, so we shoot, A LOT. Neither of my boys have any conscience about burning up my ammo, and I wouldn't have it any other way.
Couple bricks of .22, or $70 in .17hmr is a very cheap investment in time spent with them, and a chance to hopefully steer them away from some of the crap headed their way in the future.
One piece of advice. Since I'm not your mother I'm not going to lecture u on safety. My advice is make it fun. We shoot a lot of golf balls. With 10/22 you can "chase" them after the first hit. Helps to aim fast. We shoot dollar bills at 200yrd with .17. First one to hit 2 $1 corners keeps it. Make it a fun challenge.
Sorry for the novel, but I'm a HUGE believer in starting them early, shooting a ton.
From the party of HUNTIN, FISHIN, PUBLIC LAND.