How we cite our quotes: All quotations are from Star Wars: Episode VII - The Force Awakens.
Quote #1
REY: I've never met a Resistance fighter before.
FINN: Well, this is what we look like. Some of us. Others look different.
REY: BB-8 says he's on a secret mission; he has to get back to your base.
FINN: Apparently he's carrying a map that leads to Luke Skywalker, and everyone's after it.
This is the call to adventure as clearly as it can call. That's an easy sign of a character coming of age: being tasked to complete something super important.
Quote #2
REY: I didn't know there was this much green in the whole galaxy...
Another good sign of coming of age: seeing somewhere new and going somewhere you've never been before. It broadens the horizons in more ways than one.
Quote #3
HAN: You might need this.
REY: I think I can handle myself.
HAN: I know you do. That's why I'm giving it to you. Take it.
Notice that coming of age isn't portrayed as an all-at-once thing in this film. It's a series of little steps that don't seem like much at the time, but which add up to something huge.