Growing up is a gradual process, we've all been through it. But I think there is a defining moment when a young person becomes aware of what is important, where priorities should be, that their lives are in their own control and it shouldn't be wasted. This is when someone "gets it", as I call it. It's that point when Jacky Paper's "painted wings and giant strings make way for other toys".
Some people get it at a relatively early age. They focus, develop a plan and figure out what's important. Some people don't get it until later in life, you know, the person who at 40 realizes that life isn't going the way they wanted because they didn't take school seriously, partied too much, or rebelled just to rebel. Unfortunately, getting it at 40 is a tough time, not impossible to recover, but it's much, much harder and rarely happens.
I've seen the transformation of "getting it". The to-do lists, the post-it notes everywhere, making plans, asking more serious questions about the world and life. I'm not suggesting (or hoping) that 6-year olds get it; there's a lot of just being a kid that still remains when you're 6 and plenty of time to be an adult later. But at some point in high school and hopefully no later than college, kids get it. There's simply a transition time that need not come too early and shouldn't come too late. But given the choice, sooner is better.