Should be OK. The 7mm 08 is probably the most efficient of all the calibers in the 308 family.
Just don't pre-program him to fear recoil. Recoil is 80% mental, so just see where he falls into this group. People are more troubled by noise, so good hearing and eye protection are mandatory for all range work.
Get a compact scope of no more than 4X. Make it the lightest available. You need to watch the weight of the gun. Out of the box the compact weighs 7 lbs with sling. If the combination of scope and rifle exceed 7 lbs by to great a factor it will become unhandy to use and your son will not enjoy it.
For what its worth. I have the compact in 308. I had it retrofitted with the Ashley ghost ring rear and Ashely post front sight. With sling but unloaded, it goes 7 lbs. 1 oz. and is a joy to use.