I will go on a bit of a tirade here. I have 2 young girls that are 8 and 12. They have already become very successful shooters and hunters. They have made shots that I would have been jealous of 10 years ago and have killed some pretty nice bucks already. I really enjoy seeing kids hunting and shooting. It is one of the few things that doesn't use a screen and requires consistency, hard work, perseverance, problem solving, patience, and a lot of adversity. It really pains me to watch people introduce their kids to hunting and say they need to shoot grandpa's 30.06 or 12 gauge to "toughen them up." I also hate to see them try to draw a bow that is too heavy because they are "tough" and can handle it. It severely hampers their success.
I can shoot a hard kicking rifle. I HATE it! I don't shoot them nearly as well as less recoil. I was the guy that got asked to check everyone's 12 gauge slug gun because they had a flinch. The worst one was my buddies 300 win. when we were kids. It couldn't have weighed 8 lbs scoped. He couldn't get the scope zeroed. I shot 3 shots off the hood of the truck and printed about a 1.5" group at 100 yards. I measured and adjusted and put one bullet in the 2" sticker. I handed it back to him and said, "Don't ever ask me to shoot that again!"
If you have everyone hunting wear electronic muffs, you can communicate with hearing protection. Then install a good muzzle brake on whatever, and he can probably shoot it. My girls shoot A LOT. The oldest is 12 and about 75#. She tried to shoot a deer with a 20 gauge slug gun for years. The recoil was so bad she didn't even want to shoot at a deer. We bought a 350 legend and put a brake on it. She killed a deer at 215 yards that year. I believe she was 9. The youngest also killed a deer with that same rifle at 204 yards about 2 months later. She was 6. After that, we bought a 45 caliber smokeless muzzleloader. It has an obnoxious muzzle brake on it. The oldest has killed multiple deer with both the reduced load with a 300 grain bullet at 2050fps and a full load at 2650 fps. The youngest has been handling the lighter load since she was less than 50#. The brake makes all the difference. With the reduced load the recoil is about like a target load in a 20 gauge. With the faster load the recoil is about like a 3" turkey load in a 20 gauge or maybe a little more. It is all they want for the one shot it takes.
The state we live in is straight wall, muzzleloader, or bow only except for late antlerless season. We can use rifles then. We killed several deer during that season using 243 AI and 6.5 creed. The girls both shot a deer at roughly 450 yards with the 6.5 creedmoor. I used the 243AI to go 3 for 3 at 670, 640, and 610. You don't need big calibers with today's bullets and equipment.
My recommendation would be, if you don't reload already, get a 6 creed and run 108 eld factory ammo. Put a brake on it and use electronic muffs when you hunt. It will make your son more successful as a shooter when he isn't flinching from recoil. Don't EVER let him shoot without muffs and a brake. It will start a flinch just from the blast and noise.
A lot of people will tell you that a 6 creed doesn't have much recoil. A light pencil barrel 6 creed is going to have enough recoil to be disruptive to a small shooter. Even though my girls hunt with some guns that have some recoil, when they target shoot, they want to shoot the 22lr. That wins out over a braked 223. They will tell you recoil is the reason.
I would never try to teach even an adult to shoot a rifle with a hunting weight 30.06. I don't even like shooting a sub 10# 30.06 with no muzzle brake. Heavy recoiling cartridges are harder to shoot, even for guys that are very good shooters. Personally, the only time I would consider more than a 6mm or a 25 cal is if I needed the high bcs of the 7mm, 30, or 338 to keep the bullet above expansion velocity for some crazy long shot. I have personally never encountered that situation, but I know some have.
What the rokslide guys are doing with the 6um and short barrels I have done with the 243 Ackley and 26" barrels. It is crazy how easy it is to make shots and see hits. It is very common to have a deer crumple at 400-700 yards with the right 6mm bullet and enough velocity. I have not found a scenario where I considered shooting further than that at game.
Again, there is no reason to go above a 6 creed with factory 108 eldm for what you want to do. It will be the easy button. The only drawback is barrel life. It will be at least 1500 rounds. For some people that is only a few weekends of shooting. For others it is a lifetime. Please don't be tempted to have him shoot something with too much recoil. Many people suffer the effects even though it does not hurt their shoulder when they shoot.