I'm going to buck tradition, and suggest you get a 12-ga instead of the typical youth 20-ga. With today's emphasis on lighter 12-ga loads, you don't need a 20-ga for reduced recoil. With the loads available these days, a 12-ga gun can be downloaded to a 20 or 28-ga equivalent; however, if your try to up-load a youth 20-ga with hot 3-inch rounds, the recoil will be more punishing than an equivalent 16 or 12-ga gun.
If you're are concerned about a gun for a youngster, do them a favor and worry more about the stock fit (and making adjustments as they grow) than the bore being too big. I recall Olympic champion Kimberly Rhode, as a petite 11-year old, competing with a 12-ga gun.