Buy him a rifle between about 243 Win and 308 Win - all will be fine - at same time, buy at least 5 boxes (100 rounds) of ammo to blast off at targets at a range or a shooting spot. Let the kid get used to handling the ammo, reloading the magazine, unloading it - all the stuff that happens when hunting. Take a shot - get ready to shoot and then game disappears from view - what to do with the rifle and how. Really, if he has never taken a deer before, is not really that important what rifle or cartridge - he just needs trigger time and will make most anything work. You, the shooting coach, will make the hugest difference for him. If the shooting coach is not you, then get him one.
Time is passing, so our experience might not be relevant any more - my wife had never hunted - never previously shot a center-fire rifle - I bought a Remington 788 in 243 Win for her - spent many hours to file and rasp that factory stock to fit her - length of pull, circumference of grip, length of barrel - installed a Weaver K3 scope. She fired several hundred rounds at targets, at a range, before our first hunt - was a mule deer draw. About 13 or 14 years later, our son used the same rifle in the same configuration, to take his first deer - a white tail - same story - by that time, he had fired maybe thousands of rounds, but several hundred with that rifle, at targets. And then about another 10 years later, our daughter - by then married - and that rifle by then had a 308 Win barrel - took her first white tail deer with it. All were one single shot, to take their deer. When the rifle was a 243 Win, I loaded it with 85 grain Speer SPBT. When it had a 308 barrel, I loaded it with 165 grain Speer HotCor. The latest (current) loads for it are 165 grain Speer SPBT.