Star Wars' deleted Luke Skywalker introduction would depicted him hoping to join the Galactic Empire. In 1977, George Lucas kicked off the beloved space soap opera that tackled the conflict between the Empire and the Rebel Alliance. Back then, the delineation was clear between the two warring factions with the latter depicted as the good guys, while the former clearly portrayed as the villain. That said, had the film kept Luke's initial debut scene, it would've implied the story's primary protagonist was willing to join the Imperial forces.
While Han Solo was busy smuggling his way around the galaxy with Chewbacca and Leia was involved in building the Rebellion, Luke was a naive moisture farmboy in Tatooine. His life was turned upside down after he encountered C-3PO and R2-D2 as he helped the droids locate Obi-Wan Kenobi. From there, Luke finds himself on a mission to save the galaxy against the Empire and their superweapon, the Death Star. Strong with the Force like his father, his abilities gave him the piloting skill necessary to destroy the dangerous space station, making him a hero and an integral part of the Alliance.
Things could've been different based on the implication from Star Wars' scrapped original introduction to Luke. In the sequence, the young farmboy meets with his friend Biggs Darklighter (Garrick Hagon), who's in the Imperial Academy. During their conversation, Biggs informs Luke of his plans to switch sides and join the Rebellion, not wanting to be drafted by the Empire. According to Hamill, he would've wanted this whole sequence to be included in the film as it gives fans a better insight of his character - naive and clueless about what's really happening to the bigger galaxy; "he has no political persuasion" and is willing to do anything - even join the Empire if that means that it would allow him to leave Tatooine.
Luke's whole conversation with Biggs would've been a great addition to Star Wars particularly with regard to his character's journey throughout the film and the rest of the original trilogy. The movie's official cut does a good job giving fans a sense of the kind of life Luke has had until he came into contact with C-3PO and R2-D2. However, the aforementioned sequence better establishes how frustrated he is that he has to stay behind for an extended period of time so much so that he doesn't really care about how he's getting out. Starting his journey as someone who doesn't have any strong moral or political conviction between the ongoing rift between the Empire and Rebellion would've made his personal struggle to reject the dark side more interesting later on in the original trilogy.
Aside from its implication to his overall arc, this somewhat also makes him relatable for viewers. Fans initially get the impression that he's simply throwing a temper tantrum when he's told he has to stay at the moisture farm longer. The addition of this scene would have revealed how much he's left behind by his peers - even Biggs reacts violently to news that he's had to cancel his Academy application. Fortunately, this specific Star Wars deleted scene, among others, is now available to watch on Disney+.