Well, in some fanfictions, Harry might learn magic from a mysterious neighbor who is actually a wizard in hiding. This neighbor could start teaching Harry simple magic like levitating small objects when he sees Harry's natural magical inclination. Also, there could be a plot where Harry has a magical dream that leads him to start exploring his magic early. In this dream, he might be visited by a wizard from Hogwarts' past who gives him some initial magical knowledge.
In a lot of these pre - Hogwarts fanfictions, there are often plots where Harry's magic starts to manifest in strange ways due to his lack of proper guidance. For instance, he might accidentally make the flowers in the garden grow to enormous sizes when he gets angry. Some fanfictions then have him being discovered by a local magic user, perhaps an old witch who lives on the outskirts of town. She takes it upon herself to teach Harry some basic magic control and a few simple spells. This could include things like how to make a light appear at his fingertips or how to move small pebbles with his mind. It's all about exploring the idea of Harry having some early magical experiences outside of the traditional Hogwarts setting.
One interesting plot could be that Harry discovers he has magic through an encounter with a magical creature in his neighborhood. For example, he might meet a house - elf who accidentally reveals some magic to him. Another plot could involve Harry finding a hidden magic book in his aunt and uncle's attic that teaches him basic spells.
It could be a stray wizard who happened to pass by Harry's place and noticed his magical potential. This wizard might take pity on Harry and start teaching him a bit about magic.
One interesting plot could be an apprentice discovers a long - lost magic spell in the Hogwarts library. This spell has the power to control the weather within the school grounds. The apprentice then has to figure out how to use it responsibly while facing challenges from other students who want to use it for mischief.
There could be a plot where Harry's upbringing at Hogwarts affects his relationship with the other students. He might be seen as an insider by some, but also an oddity by others. This could lead to some interesting dynamics, such as rivalries or unexpected friendships. For example, he might have a closer friendship with the students from different houses as he doesn't have the same house - based prejudices that other students have.
One interesting plot could be Harry discovering a new, hidden magical ability that was not part of the original books. For example, the power to communicate with magical creatures on a deeper level. Another plot might involve Harry traveling to a different magical dimension where the rules of magic are completely different. He would have to adapt and use his skills in new ways.
One interesting plot could be that the Guardian of Magic has to protect a powerful, ancient spellbook that Voldemort is after. This would involve a lot of sneaking around Hogwarts and dangerous encounters with Death Eaters.
One idea could be that the wizarding world descends into chaos without Harry. Voldemort might rise to absolute power much sooner, and the remaining characters have to find new ways to resist. For example, Hermione could start a secret resistance group using her intelligence and knowledge of magic.
Perhaps there was a dark wizard who was on the loose in the area where Harry lived. This wizard was attacking muggles randomly. Harry, being the Boy Who Lived with an inherent magical power, was able to disrupt the wizard's spell and it backfired, killing the dark wizard. This event could be a huge shock for Harry and his aunt and uncle, who have been trying to suppress his magic all along. It would also make his entry into Hogwarts even more complex as he has already had a major encounter with the dark side of the wizarding world.
One common theme is discovery. Harry discovers his magic in unexpected ways, like finding a hidden magical object or meeting a mysterious figure. Another theme is secrecy. Since he's not supposed to use magic outside of Hogwarts yet, he has to keep his newfound skills a secret from the Dursleys.
One interesting plot could be Albus making unexpected friends on the Hogwarts Express. Maybe he meets a shy first - year who has a unique magical ability that Albus has never seen before. They then form a bond and face challenges together at Hogwarts.
There's a fanfiction called 'Early Magic for Harry'. In this story, Harry stumbles upon an old magic book in the cupboard under the stairs. This book helps him start learning magic even before he gets the Hogwarts letter. He begins with simple levitation spells and gradually progresses. It's a really interesting take on how Harry could have been more prepared for Hogwarts if he had known some magic beforehand.