I met a guy from the UK during my travels, who runs a SaaS company he started, currently operating at $1,000,000+ annual recurring revenue. He studied music and then somehow got into tech.
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On that note, I also met an 18 year old Brazilian kid who dropped out of high school (and ran away from home) at 16 and now runs a development agency and employs other developers.
Relevant qualifications will probably make things easier. But with the right mindset and hard work you can become anything in the Tech industry regardless of your background.
Tech is one of the few industries where experience and expertise are valued more than qualifications cause they wanna know, "Can you actually ship that code?" and are you familiar with the latest and greatest programming languages, frameworks, etc and not what you learnt in University 5 years ago.