Children do develop at different rates, the child’s maturity and ability to focus should be the guideline for introducing them to the next levels.

When your child is mature enough to start shooting, it is best to introduce the experience with BB, pellet or airsoft guns. These guns are not considered firearms, but they do need to be stored in a proper gun safe. Guns safety rules should indeed be followed when shooting these guns.  Take the opportunity to focus on teaching your child to correctly set-up targets with an adequate backstop before shooting. Emphasize safe range set-up, suitable targets, and to fire only when you know for sure what you are shooting at and what is beyond the target area.

Once your child demonstrates a high level of competency and responsibility in shooting with BB, pellet, or airsoft guns, plus full knowledge of firearm safety rules they are probably ready to move on to learning marksmanship and hunting!  We recommend that the next step in the transition for young hunters is to a single-shot .22 caliber long rifle. These rifles are available for a great price; they are easy to operate and a great first gun.  Make the gun theirs to maintain and clean when you are cleaning your gun.  Take them for target practice, reinforce the gun safety rules and responsible gun handling and begin to introduce the aim, trigger control fundamentals. 

We recommend taking your child for a basic rifle shooting course in your area with a trained instructor.  Here are some great resources to find training offered near you.
 
https://www.nrainstructors.org/Search.aspx

https://appleseedinfo.org/schedulemap/

If your child shows a natural ability for shooting early on, they may want to go hunting or compete in sporting events. Getting kids involved in outdoor sports is so much better for them than playing video games and will provide them with confident and responsible role models.