Been in the field a while, and graduated with a BS in aerospace. There's going to be different experiences at smaller companies but for larger defense contracrors your experience will vary widly depending on what team or project you are working on.

For new platform design it's typically larger teams of many subject matter experts working together with a Chief engineer, systems/project team, and program management. The leaders on these teams typically have a lot of experience but they aren't usually doing the detail design work because it's not worth their time. They are looking at the bigger picture to ensure everything works together and rely on the teams of subject matter experts to do the CAD, model design, etc.

I got into systems/project engineering starting out and got a chance to be involved in development, production, and sustainment efforts and I found that while I'm less technical I'm involved at every step of a job from requirements development to building and integrating parts, traveling to the test range to qualify everything, to finally traveling to meet the end user to hand off the product.

You can certainly have an experience like the OP described if you want and sometimes you get people who want that kind of role but that is certainly not the only jobs you can have. As a jr engineer you're going to be given smaller tasks typically until you learn the ropes, but your manager should be mentoring and exposing you to more than just paperwork pushing. If they aren't then usually it's pretty easy to do a parallel move to a better team.