One thing I want to add to this regarding Paradigm and force of will for spells...
I've always viewed magic use as needing those two things first and foremost. You can learn a *lot* of things without ever being "taught" them. Mechanical skills, drawing, martial arts, etc etc etc. In most cases, your talents won't be as honed as someone who has professional training, but that doesn't stop you from doing it. That said, it seems reasonable that a child can awaken and subsequently learn to toss low level spells on his/her own, just from experimentation. The advantage a child has over an adult, or even a teenager, is that their reality is already fluid and abstract. They believe anything is possible. What they believe is their paradigm. If they focus on it hard enough, they'd have the force of will, and presto, spell. The more often they do it, the easier it'd become to cast that spell.
Some here are trying to state it is flat out impossible to learn to use magic without proper education. To me, that's just crazy. Magic is a natural force in the 6th world, and something that awakened individuals can tap in to with (relatively) little effort in some cases. Shamans don't use formulas and processes to cast their spells. They use belief, pure and simple. Children, for lack of a better analogy, are all shamans in the way they think. Those that awaken later in life are probably more prone to be hermetic mages, simply because the adult mind needs the equations and how-to's of something to see how it works at that point. Belief is harder for an adult to grasp, formulas are easy.
So at least in my opinion (and thus gaming worlds), magic can manifest early without issue. It's not going to be common, but it's going to be possible, and if it's even 1 in a million, that's still about 7000 kids world-wide that can do stuff they "shouldn't be able to." The incidence of this would likely be more common in areas where belief drives everything (superstitious towns, backwoods areas, tribal societies, etc), so it's a definite possibility to consider. Maybe it never happens in your game, but it *could*, and that's enough to figure this stuff out to find out it's implications should it actually occur.