What pops into my head is to start reaching out to SpaceX. Their job posts indicate they will hire smart people and get them to work. The formal high design assurance type work from your medical experience will be a plus for sure. Step one just start reaching out.
Step two would be working on the background to explain why the medical SW experience is transferable. Know the DO-178C, DAL, ARP4754 buzzwords and flows, and I’d say even how the equivalent medical ones you are familiar with map over. This could even be a series of blog posts for you. It’ll show your communication abilities, your experience in the med side of things and then that you are working on the jump to aero.
It’ll form a good base for your knowledge, be a talking point when trying to make contacts and then in any interview. A banner at the top of the blog “I’m making the jump to aerospace, get in touch to hire me!”
But in the end at any established company, all the processes will be in place. If you join a 10 person startup then that would be tougher but that can come after a couple years at SpaceX. But I don’t have to tell you this part with your medical industry experience.
Good luck, feel free to reach out.