This is a very interesting question, as when we think of Elie in this terrifying novel, we are not explicitly told what his main aim was. As he begins his ordeal at Auschwitz, for example, the shock of what is happening takes every instinct, thought and feeling away from them:
We were incapable of thinking. Our senses were numbed, everything was fading into a fog. We no longer clung to anything. The instincts of self-preservation, of self-defence, or pride, had all deserted us. In one terrifying moment of lucidity, I though of us all as damned souls wandering through the void, souls condemned to wander through space until the end of time, seeking redemption, seeking oblivion, without any hope of finding either.
However, in spite of this moment of nihilism, Elie soon realizes how his father depends on him and how in some ways he depends on his father, and thus we can infer that his motive is survival, in spite of his desire to commit suicide that he has to conquer at various stages of this novel.