I would have to preface this answer by saying that I don't believe that Eliezer's fundamental personality and beliefs change in any definitive way. Throughout the story, he questions, and he does so repeatedly and increasingly. The experience of genocide is a cumulative one, and it is a gradual transformation that takes place within him as a result of the horror. We also have to remember that because he's an adolescent, he would be changing even under normal circumstances. What we can identify are stages and crucial points in that overall process of reaching maturity.
The first stage, I think, occurs before the Holocaust has come directly to Sighet. This is when Moishe the Beadle returns after escaping from the death convoy to which he had been sent. No one believes his story that the Jews are being massacred. Moishe has been, and still is, Eliezer's rock, in some sense, because the study of religion is so important to him. Eliezer's father is essentially absent from this part of his life. So when Moishe is disbelieved, Eliezer first sees that something is wrong with the overall benign picture of the world he inhabits.
Obviously the second stage is the arrival at Birkenau and the sight of the crematorium. Eliezer then hears the Jews reciting Kaddish, the prayer for the dead, and he says:
I don't know whether, during the history of the Jewish people, men have ever before recited Kaddish for themselves.... For the first time, I felt anger rising within me. Why should I sanctify His name ?
This unanswerable question is echoed many times, but there is no finality, no conclusion, and nothing is ever resolved. It cannot be said, in spite of his repeated inward defiance of the concepts forming the basis of religion, that Eliezer becomes an atheist. From this point, he exists in a kind of limbo between belief and disbelief.
The later, if not last, significant moment of self-discovery is Eliezer's reaction to his father's death. When he thinks, "Free at last!" it isn't so much a revelation of his deepest thoughts or of a change within him as it is a recognition of human nature as it applies to everyone. At every point, he has stayed beside his father, despite having a subliminal sense of the burden his father has become to him. It's a revelation of the survival instinct. Finally, after the liberation, Eliezer realizes that his own life has been destroyed, though he continues to live, as he looks at himself in the mirror and observes that a corpse is staring back at him.