I believe those BB's are higher velocity than what he's looking for.
My personal opinion (which may be valuable, may be worth shit, depending on who you ask) is thus: Go to Wally World. Get a $20 BB gun that comes with a few hundred BB's. If little person shows responsibility go with a single shot .22 like Steve linked. Scope that. A scope on a BB gun is like putting....a...a scope on...on something stupid. BB's are round. They change direction.
My boy is 3 and already knows the difference between his bubble gun and a real firearm. We recently had fam pics taken with the '49 Chevy we got from up north. I let him hold .22 revolver, unloaded (of course) and checked by literally 5 people who handle firearms regularly, and not once did he act irresponsible. Not saying I'd load it and hand it to my 3 y.o. EVER nor would I let him have access to any firearms EVER, but at 8 kids are smart enough to know the difference. My nephews were 8 and 9 when we took them squirrel hunting last year. Once carried a single shot .22 and the other a .410. No issues. I walked with both of them at different times. VERY responsible. They grew up on a Marine base and learned early not to mess with firearms. Their dad took them hunting SUPER young. They never got a firearm. Just went with. They learned first hand that firearms can and will kill.
Education. Use it. Discernment. Use it.
Wally World BB gun until you KNOW and are comfortable with YOUR kid and firearms. Eff what anyone else thinks or believes.
That's just me though. I'm sure others have different views or think otherwise or whatnot. That's ok too.