Can I make a switch to Software Engineering without a STEM related degree preferably in missile defense/aerospace?

My work experience is I am a quality engineer for 4 years at an automotive company. I am self learning programming, data structures and algorithms, frameworks, etc. I have a bachelor’s degree in business. I am hoping with my experience in problem solving this will make getting my first job in software engineering easier once I learn enough to apply. I understand this will take a lot of time. Will people with CS degrees always get these jobs over someone with my experience?

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