depends on the size of the boy. We started off our small nephews at 6 years old sitting in our laps with a TC carbine in 30/30 shooting remington reduced loads. Hand the boy a #1 and see if it is muzzle heavy to him. If the boy can handle the rifle well, chances are he will shoot it well. If it is a boat anchor for him to handle, then he will not enjoy it.
TC 30/30 kick very little, especially with reduced loads available from Remington. My 6 year old nephew killed three does, two hogs, a bob cat, feral dog his first year with the TC Carbine. It took him 3 years to out grow the TC, went to a 7/08 Rem 700 at 9 years old, reduced loads. I had replacement stocks that I cut to fit his length of pull perfect so he had easy target acquisition. Children also need lighter triggers than adults.
Length of pull for children is very, very short, 11"-12" max, they should be measured. 13.75" length of pull is NEVER going to fit a child where he can easily see though the scope, if at all.
Practice at the range is a wonderful thing to a young child, time with dad or uncle is never forgotten. Practice, practice, practice. My two nephews also wanted to shoot all blue jays, wood peckers, squirrels, hawks, buzzards that that saw. It was a good time to teach right and wrong in the deer stand.
We had the nephews busting clay pigeons at 100 yards before they ever got in a deer stand. They were always ready to go and shoot.