I started my grandaughter at age 5. Started her vwith a Rossi "matched pair", .22LR/.410 youth model. It was a stretch for her at first, but now that she is 11, and I painted the stock a shade of lilac and it fits just right, she is enjoying it even more. Good thing about it is, when she gets older she need not give it up, I can put an adult stock on the same gun.
I have 3 grandsons and bought each of them their first gun...plus gifted many since. Youngest one was at a gun show with me when I got him a bought him one of those accurate Chinese bolt action .22s (jw15 ?). The middle grandson got a "tricked out" 10/22 after I finished it and got some game with it. The eldest, I bought a Marlin 25N..and started him on groundhogs. He has gone on with his love of guns as a Marine Special Ops trooper and an armorer..becoming a gunsmith.
The earlier the start, the better..