I'll try to give you my perspective on working in aerospace product/systems development. First, there's no single answer that's all encompassing of the potential scope of jobs in the industry. In a company with a thousand engineers, there's probably 600 different job descriptions.
As an Aero engineer starting out, I had a view of where my career would go. The reality was pretty much something entirely different. The reality is that college taught me some basics, but what was important was how to learn, the scientific method, and how to solve problems. Engineering is just solving problems.
I've worked space systems, avionics, and weapon systems. After that, I moved into civil aviation avionics, mostly comm, nav, and surveillance. I knew development process, I had to learn the technology on the job. Along the way I was on occasion a manager.
As a manager I had to hire systems engineers. There were other managers hiring software engineers and EEs (digital design, RF design, power, etc.) and mechanical engineers (packaging). When you recruit, it's great to find 'the perfect fit' but they almost never exist. So you look for the skills necessary to do the job.
If you were to read the job postings, the would typically say: Systems engineer, must have a Bachelor's degree in engineering, physics, or mathematics from an ABET accredited university. And the it will talk about skills needed for the job (and a description of the job.) I should also point out there a number of jobs in the engineering team that don't have the title engineer. There are Analysts, Developers, Architects. A lot depends on HR decides to classify positions.
If it's a junior level position, under 5 years experience, I'm hiring based on what a coworker coined the Three "A"s - Attitude, Aptitude, Ability, in that order. Attitude is everything. I can't fix that. Aptitude is is important as they'll need to learn. Ability is good, but if they have the first two, they can learn.
Very few will have the perfect background. At higher experience levels work history is important, but I almost never had an exact match. Some did development in a non-aerospace business, others had the degree and some non-related aviation experience. So even here the 3 "A"s apply.
So the answer is read the job postings and figure out how your skills align with those listed and try fill the gaps. One quick way to gain a good basis in aviation is to take private pilot ground school. Actual flying lessons will help, but ground school will introduce you to the aviation world. And then go for it.