It could be that Mary Shelley chose this format to add a sense of authenticity and immediacy to the narrative. Through letters, it feels like the events are unfolding in real-time for the characters and for the readers.
Maybe she wanted to give the story a more intimate and personal touch. The epistolary format allows readers to feel like they're getting direct access to the characters' thoughts and feelings.
Perhaps Mary Shelley was inspired by the popular epistolary novels of her time and thought it would be a unique way to tell the story of Frankenstein. It also might have helped her explore different perspectives and build suspense as the letters reveal the story piece by piece.