You can certainly achieve this in dialogue, but you'll want to be careful that it stays true to natural dialogue. It's easy to lapse into narrative-like dialogue in an instance like this and that will feel inauthentic and forced:

"But what happened?" Mary asked.

"It was a Saturday afternoon. Dark clouds had rolled in front of the sun, so it felt closer to dusk. I was walking to the store three blocks from my house, my canvas totes ringed around my arm . . ."

See what I mean? People generally don't respond to questions with the level of detail one might include in a scene. So, if you use dialogue to convey this I information, you might find it's more effective if you're only conveying parts of the situation:

"But what happened?" Mary asked.

"I'm still ticked off about it," Glenn said. "Who expects to go to the store and lose a pinky finger? The manager said the meat counter will never be the same. Can you believe it? He's mad at me."

While the moment isn't fleshed out fully, the reader gets some of the basic details. And the conversation might continue in this way in order to reveal more. Keep in mind that dialogue should stay true to the character's voice. It's conceivable that a character is more eloquent than the way I've written Glenn. But be careful not to go so far that the dialogue sounds like narrative.

Another option is to let your character imagine her way into the moment. If she knows about it, she's bound to picture it happening. If it's important to her or strikes her in some way, she may have thought about it quite extensively. So, you could reveal the story through her perspective with the understanding that she's imagined it in this way. F. Scott Fitzgerald does this in The Great Gatsby. Nick, the first person narrator, meets Gatsby long after Gatsby's first kiss with Daisy. Gatsby talks quite a bit about his past with Nick, so he's heard about this kiss. Nick then gives us that scene in his own words, a mix of what he's learned from Gatsby and his own imagination:

One autumn night, five years before, they had been walking down the street when the leaves were falling, and they came to a place where there were no trees and the sidewalk was white with moonlight. They stopped and turned toward each other. Now it was a cool night with that mysterious excitement in it which comes at the two changes of the year... His heart beat faster and faster as Daisy's white face came up to his own. He knew that when he kissed this girl, and forever wed his unutterable visions to her perishable breath, his mind would never romp again like the mind of God. So he waited, listening for a moment longer to the tuning fork that had been struck upon a star. Then he kissed her.

You don't have to break perspective in order to cover what your character hasn't experienced. It just takes a little bit of imagination and creativity to find ways to bring the moment to life.