There's many examples you can cite for this question. Even at the beginning of the novel, Huck is exposed to abuse and violence at the hands of his father, which can destroy the innocence of childhood. But Huck's coming of age is more a rejection of the hypocrisy of the society around him. He does this in several ways: challenging the traditional gender roles (his respect for the Wilks girls shows that he values the intelligence of women), noting the discrepancy in the words of many religious people (Miss Watson's version of Providence), and most importantly, seeing Jim as a human being, rather than a lesser slave. This particular example of Huck's coming of age takes place gradually, as their friendship builds. Yet there is a moment in chapter 23 when Huck realizes that Jim cares for his family just as much as a white man would. Huck awakes to find Jim crying, and describes his reaction:
I went to sleep, and Jim didn't call me when it was my turn. He often done that. When I waked up just at daybreak he was sitting there with his head down betwixt his knees, moaning and mourning to himself. I didn't take notice nor let on. I knowed what it was about. He was thinking about his wife and his children, away up yonder, and he was low and homesick; because he hadn't ever been away from home before in his life; and I do believe he cared just as much for his people as white folks does for their'n. It don't seem natural, but I reckon it's so.
We can see how Huck and Jim's relationship has developed over the course of the novel. At first, Huck only knew Jim from the times he and Tom made fun of Jim's superstition. But now, Huck realizes just how much Jim cares for him. That in itself shows growth. But we also see a shift from before, when Huck is shocked by Jim's desire to rescue his children from slavery. When Huck first hears of Jim's plans to rescue his children, he is shocked. Huck considers Jim's children property of their slaveowner, and doesn't recognize the deep connection between Jim and his family.
Yet here, Huck's maturation is evident. He understands that Jim does indeed have the same emotions and relationships as all humans, although he remarks that it "doesn't seem natural". This is an important moment for Huck, and it sets the stage for his decision to "go to hell" instead of turning Jim in later. That in itself would be a good example of Huck's coming of age as well. His decision to refuse the "morality" of society, and instead follow his own conscience is the very definition of maturation.
This is actually well connected to a previous question about the conflict between a child and a parental figure, but I would suggest that one of the best examples is the way that Huck stands up to his father, not just by moving the money so that his father can't get it, but eventually escaping his father's clutches by taking advantage of the things he learned, being unwilling to accept a life of willful ignorance.
In doing so, he loses the boyish innocence of always looking up to one's father and being unwilling to go against the parental will.