I would argue that the exposition in this story goes on for quite a bit longer than it does in most other stories. Sammy, the protagonist and narrator, experiences a conflict with his manager, Lengel. Lengel does not even actually appear in the story until more than halfway through. He comes in from the parking lot after haggling with a seller of cabbages and sees the group of young girls that Sammy has been eyeing and describing this whole time.
When Lengel tells the girls that the grocery store "isn't the beach," we have our inciting incident: the event that initiates the conflict within the story. Sammy takes issue with Lengel's embarrassing of the girl he refers to as "Queenie," leading to the climax where he quits his job at the A&P. Therefore, everything prior to Lengel's reprimanding of the girls could be classified as exposition: Sammy sees the girls walk in, describing each of them in turn, and he makes a mistake with another customer as a result of his distraction which he must fix. He watches as the girls make their way around the store, commenting on what they wear, their hair, their bare feet, and so on, until they finally come to his checkout counter where Lengel sees them. All of this is exposition, background information we need to help us understand the conflict.