I was 2 yrs when I got my first gun a Marlin 336c 30-30 from and uncle who willed it to me.It was fallowed with a 20ga. J.C. Higgens single shot @ 7 yrs that used to kill gophers around the farm.

I bought my Daughter a Rossi matched Pair 22 lr/.410 for her 5 th birthday and she can hit gophers @ 50yds.
It is all up to the adult,I gave one nephew a 22 @10 yrs and another a 12 ga. Rem 1100 when he was 9.