The good news is that there are more great options than ever for kiddos. I would look at chassis rifle offerings that come with a six position AR style stock. I don't keep up with factory rifle offerings these days, but it seems like I've seen several that would fit the bill nicely. Another option would be to take a rifle you already own and drop it into an MDT LSS chassis or perhaps a Manners Compact Stock (MCS-CS or MCS-CS2).
When my son was 7 I decided to bite the bullet and go ahead and have him a custom rifle built. I tried to do so in a manner that would grow with him basically forever, with a lot of optionality for upgrades as he grows and develops as a hunter. I went with the following:
Zermatt Origin Short Action - Interchangeable bolt heads
WTO Switch Lug - Change barrels in about 2 minutes or less
Proof Carbon Barrel - 6mm CM, 1:7.5", 16.25" finish length
Timney Trigger
MDT LSS Chassis with Magpul CTR Stock with cheek riser (6 position AR style adjustability)
AB Raptor 4 Suppressor with 4" Reflex (7.62)
Salmon River Solutions Arca Pic - tripod mount on arca & pic for bipod
Hawkins Precision Rings
Leupold VX5 3-15x44
We currently only have the one 6mm CM barrel. However, as his quarry grows we are only a barrel and perhaps a bolt head & mag (depending on caliber selection) away from stepping up to a very capable rifle for Elk sized game.
At 10 years old (currently), he has accounted for 6 whitetail, a blackbuck, a Texas exotic sheep & a pronghorn, as well as dozens of hogs with this setup. He can also hammer MOA steel out to 600 with surprising consistency, as long as Ol Dad gets the wind calls right.