Hi there! I know Legacy is the wealth of info on the insider track here, but figured I would throw my two cents in here as well, mainly because we have eerily similar backgrounds, haha. I also was a mechanical/aerospace engineering major in the north east with dreams of the themed entertainment industry (graduated in 2015, decided not to stay for my MEng), and I can say without a doubt while an engineering degree on paper is impressive, it is entirely on your own shoulders to really spruce up and develop your portfolio when it comes to more design related things. If your curriculum is anything like mine was, you sure as hell aren't going to find too much portfolio fodder just in class alone, haha.
I ended up doing a minor in theater production while I was there, so there were a lot of design classes that came packaged into that that are very key to attraction design (lighting, set design, even costume design). I was fortunate to be able to use these as required credits for a couple of the liberal arts credits we were required to take, but if your school offers any theatrical design classes, definitely see if there is a way to weasel them into your existing schedule. If they aren't going to overload you, take them anyway. Outside of class I helped start what would eventually become a TPEG chapter on campus (Theme Park Engineering Group), but sadly I really only played an advisor role, because it only finally got off the ground my senior year. There are a number of armchair imagineering contests that pop up through the year, so getting a small group together to collab and enter a couple would definitely help start you down the path to developing a good backlog of design work.
Since graduation I have worked a more traditional engineering day job, having moved to New England (we actually do a lot of custom signage for the parks though, weirdly enough), but still have continued in the theater and haunt world outside of work hours. I have found a lot of opportunities to flex my set and lighting design muscles in the community theater scene locally, and do commission work for cosplay and theatrical costumes. My friends and I have also run a small haunt in Brooklyn together for a couple years now, and have really used this as a space to explore and develop our collective skills when it comes to shop drawings, draw-downs, build schedules, story treatments, the list goes on and on.
Depending on what aspects you find yourself most drawn to about the industry, definitely take a look around to find official documents (they are out there... trust me, haha) and try and pick them apart. Understand why they look the way they do, what information they have on them and why, and then apply those same principles to a personal project. Building a small coffee table for Uncle Stan? Make a set of shops for the build, including callouts, elevations. Doing a small background flat for a community theater production of Annie? Make a reference drawing, do some sketches, and take pictures to document your process. The more you can practice doing things in the manner design documents are actually made, the better prepared you will be/the more valuable you will be, if not solely from simple familiarity with the design flavor.
The biggest thing I can say is, while HHN is an amazing event, and obviously I myself would jump immediately if any opportunity arose to be a part of it, I think it helps to realize that there are so many opportunities to do this kind of work out there that aren't directly for Universal too. Realizing how small the team truly is can be a shocking and somewhat disheartening thing to hear for the first time, but it can also be seen as a good thing too. The sheer number of collaborators that work with the team to bring the event to life (freelancers, contracted build teams, etc) mean there are that many more paths to explore, if your goal is truly HHN or bust. If you have a passion for this kind of work though, plain and simple, there are so many different outlets to explore outside of the event. Working with my friends to bring our little haunt into a more commercial space has been incredibly exciting, and while it may not be HHN, we do it for the same reasons and with the goals in mind: making people scream, smile, and maybe inspire them in turn.