What type of big game are you going after? Price range(new or used)? Finally, is this an "average" size 12 year old? I would start with a .243 caliber, then work your way thru to .270; Have you any friends with guns he can try out concerning the recoil?

I don't think a .30-06 is a good first gun for any 12 year old, even the Shaq Daddy when he was 12! A .243 or a .30-30 with Managed Recoil / reduced recoil loads, which are about like a .243 Win would be a better choice. Definately a single shot or bolt action, no lever guns or autoloaders for beginners.

the 243 win is a good starting rifle ,but, for the same amount of recoil, try a 260 rem.

I would have to go with a 243 or 25-06. My 10 year old shoots a Remington 25-06 with no problem. Flat shooting and accurate. Not much recoil from this gun at all

I say start kids out with lighter rifles with less recoil. Go with a .243 or a 25-06. that's the range of calibers i recommend because they produce speed and accuracy, as well as knock down power. The 25-06 produces the flat bullet and speed of a .243 along with the knockdown power of the .270. It's a pretty serious caliber and it does not produce much recoil at all. Kids could shoot it all day and wake up the next morning without a stiff shoulder.

Borrow some rifles and have him try them if you can. Start out small. Make sure you use hearing protection, the sound can make the recoil seem worse. See what he likes.

If you had to just go and buy one right now, get a Marlin XL-7 in .25-06, and you have everything but elk, moose, and bears covered. Some guys use a .25-06 on elk, but that's another story. Mount a Nikon Buckmasters 3-9x40 or Leupold VX-I and you will have spent less than 550 dollars for the whole deal. That's the least you can possibly spend and have a legitimate big game setup, and in this case, you will have a very solid one.

If he can handle it, get it in .308 or .270, then the elk, moose, and (black) bears are covered too.

243 or 257 roberts are the way to go. My son loves his savage model 10 with iron sights, and a wood stock in 243, he's almost 6. Has to shoot it off a rest, and with earpro in he doesn't notice recoil, basically noise is more of an issue than recoil, so he gets plugs, and muffs, and stays happy. I wouldn't hesitate to use that same rifle for a 12 year old, or a vanguard youth model. Given my son's apparent noise sensitivity I'd be real reluctant to get him a muzzlebreak.

Don't get a .25-06, 7mm-08 I think is about the perfect cartridge for a young hunter, good power, decent bullet selection, mild recoil, short action (short actions fit the frame of smaller shooter's better), it's damned near perfect from my perspective

PS

The best Moose kill I ever witnessed was a 17ish year old with a 30-06 with over the counter Remington 180 grain 30-06. Nothing special, just the ability to hit "MOP"!