IMHO, everyone should work towards attaining basic marksmanship skills before shooting at a live target. But lets dispense with idea of MOA as an index of the accuracy necessary for big game hunting. A more useful index should be based on the target size, which tends to be 12"-16" on deer sized game. Provided you can keep your rounds within 8" at a given range, that is sufficient for a positive outcome. The opportunities a hunter has in thick cover is weighted towards the off hand position, but if you can use a natural rest to support the rifle, your chances of making a first round hit on a stationary target increases dramatically. But in the bush, where the range tends to be short, and the action can be fast, so marksmanship must be balanced against time.
Begin your practice at short range, say 25 yards, shooting off hand. Shoot pairs, working the action of your rifle as quickly as you can between shots. When you become comfortable with that, move back to 50, but now introduce kneeling and seated positions to your off hand. From here you go back to 100, where you can also introduce prone to your positions. If you can continue to increase the range until you can no longer keep your rounds within 4" of your intended point of impact, which defines your maximum range.
Work at getting onto the target quickly, get a repeatable cheek weld, and press the trigger, don't slap it or jerk it. If you find your aiming point swinging off the target, don't decrease weight on the trigger, just wait for the sight to come back to center, then increase the pressure until the shot breaks. With practice, this can be accomplished quickly. Keep at it, and don't get discouraged. Dry firing at home will be beneficial to improving your target acquisition, sight alignment, and trigger control.