Ruger American compact, or Rem 700 youth if you can find one used.

We got my son a 700 youth in 708 and it is one of our favorite rifles. Even big men love to shoot it. Nowadays I would probably consider a 260 or creedmoor, but you can do much worse than the 708 and it's widely available in youth/mountain rifles.

Howa used to have some nice compact rifles, and they have a micro action available in Grendel which many people love as a super mild recoiling combination. I would pick Grendel over 7.62 x39, a bit more steam and shoots much flatter. The CZ micro actions are also available in Grendel.