Perhaps Harry is rescued by an unexpected character, like a centaur who has been secretly watching over him. The centaur arrives at the Dursleys' on a moonlit night, and using its natural magic and knowledge of the stars, it convinces Harry to come with it to a safe place in the Forbidden Forest where he can be protected and trained.
One possible scenario could be that a powerful wizard or witch, perhaps someone who knew James and Lily Potter well, comes to rescue baby Harry. They might use magic to bypass the Dursleys' defenses and take Harry away to a safer place, like a hidden wizarding community.
In this kind of fanfiction, perhaps Harry is rescued by the Order of the Phoenix earlier than in the original story. They might have realized the Dursleys' mistreatment sooner. Then Harry could start his magical training earlier, away from the hostile environment of the Dursleys' home. He may also form closer bonds with other members of the Order, like Sirius, who could play a more active role in his upbringing.
One possible scenario could be that the Dursleys, out of their long - held hatred and jealousy, manage to poison Harry's food. In the fanfiction world, they might find a way to obtain a powerful and undetectable poison. Another could be that they stage an 'accident' like a fire in his room while he's asleep. They could block his escape routes and let the fire consume him.
One possible scenario could be that Harry uses his magic skills in a creative way to escape. Maybe he creates a diversion with a spell to distract the Dursleys and then slips away unnoticed. Another could be that he gets help from an unexpected ally, like a friendly magical creature that guides him out of the house.
Hermione could be the rescuer. Maybe she discovers through her research that Harry is in a bad situation at the Dursleys' and decides to take action. She uses her intelligence and magic skills to break into the Dursleys' house and get Harry out. Then they would go on an adventure together, and Hermione would be like a mentor to Harry in a way, teaching him things she has learned from books.
It could be Dumbledore. He might have realized that the Dursleys were not the best place for Harry after all and decided to take matters into his own hands, using his powerful magic to rescue baby Harry.
One scenario could be that Dudley gets turned into a frog. It would be a fitting punishment for his years of bullying Harry. Another could be that the Dursleys' house starts to have strange magical malfunctions, like the stairs turning into a slide, constantly tripping them up.
One scenario could be that Bill uses his charm to charm the Dursleys into letting Harry go. He might be really smooth - talking and make them believe that it's in their best interest to send Harry away with him. Maybe he offers them some sort of compensation in the wizarding world, like a magical object that will keep their house clean forever.
One possible scenario could be that Harry discovers a hidden magical passageway in his tiny bedroom at the Dursleys'. It could be a secret portal created by a well - meaning wizard long ago to help any oppressed magical being in the Muggle world. Harry stumbles upon it while looking for a lost sock or something mundane. Another scenario might be that a group of friendly magical creatures, like house - elves, conspire to help him escape. They create distractions around the Dursley house, like making the pots and pans fly around and creating chaos, which allows Harry to slip away unnoticed.
Well, perhaps in the fanfiction, the Potter family has some allies that help them in rescuing Harry. For example, they might team up with some powerful but little - known magical families. Or it could be that Lily Potter has a special connection to Harry that leads them to his location even when he is hidden away. They could then use a protective spell to keep him safe from further harm.