A 20 Gauge slug will produce 30 + lbs of recoil in a 7.5 pound gun depending on the specific load. That is higher than most 30-06 rifles even light ones. I would get the kid an 06 and start him out on the federal or remington low recoil loads.
These cartridges have ballistics equal to the 30-30 and are effective to approx 175 yards on whitetails. Keep in mind that most 06s are heavier than the 30-30 lever actions typically used in that cartridge and recoil should be nill.
This way the kid will have a gun he can get the full performance from when he can handle it. It seems like not many hunt with the first gun their father got them because they feel it is under powered once they are grown up and can handle more recoil.