Early in the story, the narrator goes to find metal with his father, a priest. When his father gives him the metal, he holds it and does not die. This superstition indicates, according to the narrator, that he is truly his father's son and would be a priest:
He gave me the metal to hold—I took it and did not die. So he knew that I was truly his son and would be a priest in my time.
This seems to indicate initial proof: that the narrator would or could become a priest because of two possible conditions: 1) He was truly the son of a priest and 2) He could touch metal and not die. After some time, the narrator was permitted to search for metal himself, evidently the work of a priest.
But it seems that the narrator also had to go on a journey to assure that he would become a priest. When he returns from the journey he is purified again and, judging from his father's statement, this is the final proof that he has become a priest:
When I saw my father again, I prayed and was purified. He touched my lips and my breast, he said, "You went away a boy. You come back a man and a priest."