Past the age of 2-3yrs old, I recommend highly against the Cricket rifles. They aren’t expensive, but they outgrow them SO fast.
I have had the pleasure of instructing kids for a long time - which means introducing them and their parents into firearms safety and marksmanship development. Kids learn and grow MUCH faster than we give them credit, and it’s irresponsible and illogical to consider handicapping them with a single shot rifle does anything to instill discipline. Single shots don’t force kids, or even encourage them, in any way to only squeeze when the sights are on target. Instruction, coaching, and consequence are what instill discipline - just like any other aspect of raising and teaching a child. If you don’t want a kid to run in the house, you don’t tie his shoelaces together so he can’t run. You tell him not to run, and apply consequences if he doesn’t listen. If you want a kid to only fire when he’s on target, the same applies. Having a repeater allows them to better work other skills than just reloading their single shot over and over. Recoil recovery, regaining sight picture, follow through, target (re)acquisition, transitions, etc. REALLY difficult to work on these without a repeater. We teach kids to crawl, walk, run, jump, climb, ride a bike, roller skate, play football, wrestle, play baseball, basketball, ice skate, read, write, etc etc etc all within a few years. Marksmanship skills don’t need to be governed just because someone thought a long time ago a single shot Rascal or Cricket was a good idea.
Having that experience, I bought my son a Savage Mark II and a Marlin 60 when he was 2, got aftermarket stocks and cut them down to fit his LOP, and added cheek risers to rise him up to the sights. A red dot scope with an integral laser pointer helps show the parent/instructor where the rifle is aiming, and it’s super easy for the kid to learn to “put the dot on the target and squeeze the trigger slowly.” Firing from bags/machine rest, of course, and Rule #1 is “don’t pick up the rifle.”
He’s 5 now, shoots an AR from shooting sticks, and has been transitioning into iron sights and into scopes, replacing his RDS for longer range shooting. He’s building his own AR this winter, and we’re working on deciding what centerfire bolt gun he’ll build this coming spring/summer (leaning towards a 243 LBC CZ or Howa).
Starting with these full size firearms, then replacing the stock temporarily, instead of buying a Cricket or Rascal which will only be useful for a couple years of their extreme youth (and arguably not very useful even then) makes a lot more sense to me. Both functionally and financially.