The following contains spoilers for Solo: A Star Wars Story. Bookmark this and come back after you've had a chance to see it.
Solo: A Star Wars Story creates a life for Han Solo before the events of Star Wars: A New Hope, but it also creates a corner of the Star Wars galaxy we've never seen before. Since this part of the Star Wars story had never been told before, screenwriters Lawrence and Jonathan Kasdan played with different ideas about how certain parts of the story would play out. Jonathan Kasdan told CinemaBlend that at one point, when Han decides to join the military as a solution to avoid capture, exactly which army he was joining was left up in the air. One idea had Han potentially joining up with a different army but eventually finding himself in a very familiar uniform. As Jonathan Kasdan explained...
There was an incarnation of this script early on, a thing that I loved. He joined up with the army, and we weren't clear exactly what the army was gonna be at the beginning. We thought maybe it would be the Corellian army. We were playing with this idea of people being thrown into wars like Vietnam, and they just don't know what their job is gonna be. At one point in the scene, and this was a great thing I'm sorry we lost, a big senior officer says, 'You're all gonna be much safer from now on because you're going to be wearing these.' And he smashes down a stormtrooper helmet. There are great ideas, and they were all through the movie and contributed by all people that get peeled away as you try to create a lean story that is on point.
In the final cut of Solo: A Star Wars Story there's no question that Han is making the decision to join the Imperial Navy, expecting to be a pilot. That doesn't work out for him, and he ends up a soldier on the ground. However, it seems that at one point the movie was going to be more vague about where Han was joining up. It would have been made clear to him, and the audience, when it was revealed he would be expected to wear a Stormtrooper's uniform. Which would have caused us to look at the sequence in Star Wars: A New Hope when he put one on a little differently.
This certainly would have been a cool reveal in the moment, though it's understandable why the decision was made to change it. As Jonathan Kasdan says, eventually you need to start stripping away the parts of the story that are unnecessary so the movie doesn't get bogged down. As cool as this reference would have been, Han's time in the Imperial army really only exists to get him to the location the story requires, making the details much less relevant.
While the Stormtrooper helmet didn't make it into the final cut, there are numerous fun and interesting Star Wars easter eggs and references in the film. You can see them all in Solo: A Star Wars Story in theaters now.