Well, they might become friends. Maybe they discover they have a shared interest in magic even before getting to Hogwarts. For example, they could both be fascinated by magical creatures and exchange stories about the ones they've read about.
A magical creature could also be an important character. Imagine a friendly house - elf that they meet. The house - elf could be in some sort of trouble, and Harry and Daphne decide to help it. This adventure with the house - elf could shape their relationship and also introduce them to different aspects of the magical world.
Maybe they attend a pre - Hogwarts magic class together. Harry struggles a bit with some of the advanced spells being taught, and Daphne, though initially a bit aloof, decides to help him. This could start a relationship where they learn from each other, with Daphne learning about Harry's unique experiences outside the wizarding world and Harry getting a better understanding of the pure - blood society through Daphne.
One possible plot could be that they meet in Diagon Alley. Maybe Harry is lost while shopping for his school supplies and Daphne helps him find his way. This could start a friendship where they exchange stories about their expectations for Hogwarts. It might also be a chance for Daphne to see Harry as more than just the famous Boy - Who - Lived, and for Harry to make a friend outside of the Weasleys and Hermione.
If they meet before Hogwarts, they might already have a sense of loyalty towards each other. So when they get to Hogwarts, they could look out for one another. For example, in a dangerous situation like a run - in with a rogue magical creature, they would be more likely to help each other compared to if they were just acquaintances. This pre - Hogwarts meeting could also mean they have inside jokes or shared memories that make their Hogwarts years more enjoyable.
Maybe he meets an old Canadian witch who has a lot of wisdom about a certain type of magic that is rare in the UK. She could give Harry some valuable advice or a magical item that helps him later at Hogwarts.
One possibility is that they meet in Diagon Alley. Maybe Ginny is there with her family, getting her school supplies, and Harry just happens to be in the same shop. They could share a brief moment, like a shy smile or a simple hello. This encounter could be the start of a pre - Hogwarts friendship that they keep secret until they meet again at school.
One possible plot could be that they meet during a wizarding event in France. Fleur, being from a French wizarding family, might be at a magical fair. Harry could be there with the Dursleys on a 'family' trip (forced by the Dursleys to go to France). They accidentally cross paths and Fleur, sensing Harry's unique magical aura, strikes up a conversation. This could be the start of an interesting pre - Hogwarts friendship.
They might become fast friends. In some fanfictions, they could discover their shared love for magic books even before Hogwarts. This early encounter could lead to them sharing secrets about their strange magical experiences prior to school, like Hermione telling Harry about her accidental magic incidents and Harry sharing his strange encounters with the Dursleys. This would strengthen their bond and perhaps make their Hogwarts years even more intertwined.
In some fanfictions, they might initially dislike each other. Draco, with his pure - blood supremacist upbringing, could look down on Harry. For example, he might make snide remarks about Harry's lack of knowledge about the wizarding world. However, this early encounter could also lead to a different dynamic later at Hogwarts. Maybe Harry would be more prepared to face Draco's taunts because of this prior meeting.