This question might be better suited for the workplace stackexchange. That said:
Short answer: Technically, yes. While a degree is important, it's possible to get a job without one.
Long answer: It's a long uphill battle. When a company is hiring someone, technical qualifications are obviously one of the key things they look for, although in my (albeit limited) experience, it's often secondary to "soft skills". Unless the company is looking to fill a specifically highly-qualified position like "Senior developer" or some sort of leadership role, a prospective employee's capability to be a good team player, ability to learn, and motivation level are more important. A company would (typically) hire someone who is nicer/a better team-player/willing to learn over someone who doesn't have those traits but is better with the technical skills. Basically, the calculus is that it's easier to train someone's technical skills as opposed to training someone to be a nicer person.
That said, lacking a formal education in a highly technical field like "aerospace software development" is going to be a huge impediment to getting hired. This means that unlike all the other applicants, you will need to go to extensive lengths to prove that you have the technical competence required. A degree is a shortcut to this, and without one, you will need to either:
- Have a professional history in software development. For example, if I were Aerospace company XYZ looking to hire a software developer and it turned out that while they didn't have a degree, they've worked for 8 years as a developer at Generic Software Company ABC, I would be willing to give them a chance
- Have a successful personal history in software development. For example, if the company asks what qualifications you have if you don't have a college degree and you say, "Oh, I'm the creator of the popular open source software XYZ that has over 200,000 downloads on GitHub and here's my commit history" that would get your foot in the door
- Connections. If you know the right people who can vouch for you, you can get almost any job
This is, of course, not every possibility, but "aerospace software development" is a rather high-end career field and has high standards because the code that people write often ends up with directly ensuring the safety of people's lives.
Also, not to be too much of a downer, but it takes serious grit (not to mention years) to become a programmer good enough to be hired through self-study alone. Furthermore, even if you do become a competent programmer through self-study, companies are often leery to hire people like that because while their technical skills might be good, a large part of software development concerns teamwork and project management which self-study doesn't have.