One idea could be that baby Luke Skywalker time - travels to the era of the Old Republic. He could end up being found by a Jedi Master there and starts his training much earlier. This would completely change the course of the Star Wars timeline as he'd be much more powerful by the time the original trilogy events are supposed to occur.
Another possibility is that baby Luke travels back in time to the Clone Wars. He could be a mystery to the Jedi Council at that time. Some might see him as a threat, thinking he could be a Sith plot. However, others, like Yoda, might sense his strong connection to the Force and take him under their wing. This could lead to different alliances and strategies during the Clone Wars, and also have a huge impact on Anakin's path, as Luke's presence could influence Anakin's decisions in some way.
In a time travel fanfiction, baby Luke might travel to a future where the Sith have taken over completely. His innocent presence could be a symbol of hope for the remaining Jedi and resistance fighters. They could see him as a chance to rewrite history and prevent the Sith's rise in the first place. Since he's just a baby, they would have to protect him while also trying to figure out how to use his potential to turn the tables on the Sith.
If baby Luke time - travels to a post - apocalyptic future in the Star Wars universe, he could be the key to rebuilding the Jedi Order. His very existence could inspire the survivors to start anew. They might look at his pure connection to the Force as a sign that there is still hope for a better future, and they would protect and train him to become a great Jedi, changing the fate of the galaxy once again.
Another interesting plot is Luke traveling to the future. He discovers a galaxy in chaos due to a new, powerful dark force. He has to adapt to new technologies and new forms of the Force while also finding a way to defeat this new threat. He might meet descendants of his friends and foes, which would add an interesting dynamic.
A really interesting plot would be if Luke's time travel was accidental and he ended up in a parallel universe. In this universe, the roles of the Sith and the Jedi are reversed. He would have to figure out how to get back to his own universe while also dealing with the strange new world he's in. Here, he might learn things about the Force that he never knew before, like different ways to use it that are unique to this parallel universe.
There could be a fanfiction where baby Luke Skywalker is visited by a mysterious Jedi in his dreams. This Jedi gives him some sort of premonition or a message about his future. It could be a Jedi who was friends with his father and is trying to guide Luke from afar, even at this young age.
One idea could be Luke traveling back in time to the Clone Wars era. He could meet his father, Anakin Skywalker, before his fall to the Dark Side and try to prevent it. Maybe he uses his Jedi skills to influence Anakin in a positive way, like teaching him some advanced Jedi techniques that could strengthen his connection to the Light Side.
One idea could be Luke traveling back in time to the Clone Wars era. He could meet Anakin Skywalker before his fall to the Dark Side and try to change his fate. Maybe he'd use his knowledge of the future to prevent certain battles or alliances that led to the downfall of the Jedi Order.
When traveling to the future, Luke could become more desperate. Facing a world in chaos or a new, powerful enemy, he'd have to quickly adapt and find solutions. This would make him more willing to take risks and use powers in ways he hadn't before. His view of the Force might also expand as he encounters new forms of it in the future.
Protection is a common theme. Since he's a baby and the son of Anakin Skywalker, many fanfictions focus on how various characters like Obi - Wan, Beru, and Owen protect him from the Empire. For example, Obi - Wan might use his Jedi skills to hide Luke's presence.
One great 'Luke Skywalker as a baby fanfiction' could be about his early days on Tatooine being secretly protected by Obi - Wan. Maybe it focuses on how Obi - Wan made sure Luke was safe from the Empire's reach while also trying to figure out how to train him in the ways of the Force when he grew up.
One idea could be a crossover where Luke Skywalker somehow ends up in the wizarding world of Harry Potter. Maybe he crash - lands his X - Wing near Hogwarts. The Hogwarts students are amazed by his use of the Force, which they initially mistake for some new form of magic. Harry Potter could team up with Luke to fight a common enemy, perhaps a dark wizard who has also discovered some ancient Sith knowledge and is trying to use it for evil in the wizarding world.