What is the exposition of John Updike's "A & P"?
I assume that you mean "exposition" for the rather curious usage of the word "initiation" and so I have edited the question accordingly. Let us remember that when we think of the plot structure of works of literature, we can define the exposition, which is the first element of the plot structure, as the part that introduces the main characters and the conflicts that exist, either internal or external. Thus, when we think about this excellent short story by John Updike, it is clear that the central conflict is introduced by the very first line of the story:
In walks these three girls in nothing by bathing suits.
Clearly, during the conservative times in which the story is set, this was a major shock in terms of what is acceptable behaviour, and so this introduces the conflict as we see what will happen to these three daring girls. Likewise the first paragraph introduces us to the narrator, who tells the story, and who clearly shows his cynical approach to his work by referring to the customer he is serving as a "cash-register-watcher" and a "witch" who delights in giving him "hell" because he rang up an item twice.
This then is the exposition of this story. How the conflict will be resolved is shown towards the end of this tale.