Each child is different and is ready at a different time. I would say 6 to 12 years.
Why do you say "boys"? My daughter is 10, went hunting with me since she was 4.
She started shooting 10-22's when she was about 6, 410's at about 6 1/2.
She has had her own 10-22 for about 4 years (with a nicer scope (Leupold) than mine)
She has had her own 20 gauge (still has not shot it but it is hers) for about 3 years.
We are going out target shooting tomorrow and she is taking a girlfriend who is 11.
This girl has never shot and is against hunting. We have been explaining for a couple years where chicken strips, cheeseburgers, leather belts and shoes etccc come from.
Her dad is a city boy who has never been aroung guns at all and was against it at first. (He is the Dad so it was not going to happen) After she asked somemore and spoke with the Mom, Dad was convinced. Mom grew up in Michigan shooting and hunting and explained it is very safe and fun.
I will start her on a 22 rifle and take it slow with a lot of safety talk first and then one round in the firearm at a time. If she does well we will shoot a .410.
I say again each child is different, but exposing them to firearms at an early age is a good thing!
Some are ready at 6 ot 7 some are not. My daughter is still too small to shoot offhand with the heavy barell 10-22, but she could do it all by herself (line up sights, and pull trigger) several years ago as long as it was on a 5 gallon bucket with a backpack or jacket.