How does the author show us that Ralph is finally beginning to face the realities of their existence?
In the beginning of the story, Ralph is content to play and sees their plight in terms of being free from adult intervention in his life. The idea that he (and the others) can do as they wish is not only intriguing to him, but rather liberating. It slowly dawns on him (with Piggy's influence), that he's destined to become the reluctant leader. Over time, Piggy is able to open Ralph's eyes to the reality that he (Ralph) must assume a leadership role. While Ralph is, at first, reluctant to assume the role, he nonetheless, realizes that his best interests (rescue) are best served if he serves the best interests of the group as well.
Ralph follows Piggy's advice to use the conch as a way to summon the others and comes to realize the role that the use of the conch can serve as a means of maintaining some semblance of order.
Ralph also comes to reluctantly accept Jack's assertion that procuring food as a key element to their survival. While he doesn't necessarily agree with the passion of Jack's pursuit of the hunt, he does come to respect Jack's efforts, however misguided they appear.
Finally, in the face of their society's disintegration, Ralph presses ahead, keeping in mind the end goal of being rescued. He goes from an initial "immaturity" to a grudging acceptance that he has no other alternative than to press ahead against the odds. This takes a maturity that, while thrust upon him, should be regarded as a worthy endeavor.