I have emphasized my ability to ship. I have never gone to a potential employee and said "hey trust me, I can do it even though I don't have proof."
Rather: "Here is the work I've already done, and I can do the same for you, or better."
I stayed at the first company for 3.5 years. During that time i also spent enough time on the then-young Stack Overflow to get 30-40k reputation. I have a solid degree in a technical but unrelated field. And i'd like to think i'm actually a decent programmer, and that this comes across in interviews. All that added up to make it pretty easy to get the next job in the normal way.
I’ve hired CS grads and they need at least a year to learn how things actually work in practice rather than what they’ve been taught. Often this involves taking the simpler path rather than the more complicated one that immediately occurs to them. This is fine, BTW.
I learned by trying to build a few different things and hacking them together until it worked.
I had many late nights of watching youtube videos and reading tutorials to try to understand more complex stuff. I remember seriously questioning if I'd ever get better.
8 years later and I'm a Senior Software Engineer in an incredible team at an exciting company. It's possible!
Maybe if demand were low for programmers, degrees would matter a lot. It is a way to weed out people if you have too many applicants. But demand is high, and supply (from what I understand) is relatively low. So work on selling yourself. I imagine people's github profiles mean more than a degree does these days.
But please note: I am an American former programmer, so take what I write with a grain of salt.