Since it was taken for granted within both the Established Church and the Catholic Church that university would provide an opportunity for a student’s faith to mature and flourish, Newman did not need to persuade anyone about it. For this reason he does not write about it explicitly.
Little is known about Newman the undergraduate and how his faith developed, though he does refer to this in his Apologia; it can also be discerned in his (largely autobiographical) novel Loss and gain.
We are better informed about Newman the tutor and how he saw the task as one of spiritual oversight.