Check local clubs to see what shooting sports are offered. Just because they are open to all ages doesn’t mean youth can’t participate. Many clubs fully support and encourage youth participation. The trick is to teach them basic firearm handling skills and common competition rules first. Once you are confident they can handle a firearm safety and know the rules that will get them DQ’ed, start in simple matches with simple gear, like steel matches or GSSF. Once they are comfortable under match pressure and a timer, move into USPSA, ICORE or IDPA before 3 gun.
I have seen youth start in USPSA. While proper coaching can get them to be successful, I have seen them get upset and never return from the pressure. It all depends on the youth and who is coaching them.
Also, don’t forget about high power, bowling pins, bullseye pistol, cowboy shoots, and black powder.