At the time of telling "Araby," is the narrator a young or a growing person?
This is an interesting question to consider. Firstly, let us note that the story is told in the first person, by the boy himself who experiences such a significant epiphany in his adolescence. In addition, let us also be aware that the story is told in the past tense:
On Saturday morning I reminded my uncle that I wished to go to the bazaar in the evening.
Note the use of the first person in "I reminded" and also the past tense in "reminded" and "wished."
Therefore it is clear that the narrator is looking back on his youthful past as he tells this story. However, what we are not told is how old the narrator is as he tells this story. We can perhaps infer that he is telling this story in his later years, because we can guess that anybody would have needed a significant amount of time to process such an experience and its importance, and what he could have learnt from it. However, no clear indication is given in the story.