Five years ago I would totally agree. Now, when you do not want to share your fun thoughts with a border guard; a police person; an AI scavenger; a random jerk -- I would say, having a safe-ish space becomes almost a necessity
This article -- esp. the "In literature" section -- is one of those Wikipedia hidden gems which leave you amused but also worried for them being one day thoughtlessly pruned by some Paladin of Significance
It's fairly possible though for a non-EU citizens. I moved to Sweden from outside EU when I was 36 with a family (got job as a developer). It took 5 years from work permit to Swedish pasport.
I was in a pretty much similar situation to you when I started to think about moving to Europe (or Canada, btw): some work experience; no formal degree; late twenties. I also felt there is some chicken and egg problem, though the solution is simple: just send your CV to interesting companies, asking if they are offering relocation from outside EU. Many large companies like Spotify, Klarna offer relocation, as well as meny smaller companies.
As you have went through recruitment process (which in Sweden is quite humane) and accepted the offer, your employer would have applied on behalf of you for work visa (typically 2-years, which later could be extended unless you get a permanent right of residence after four years).
In Sweden there are plenty of jobs and if you have several years of working experience no one is asking for your degree. Jobs with relocation option could be found, among others, on Stackoverflow or on local labor agency website (Arbetsförmedlingen [1], in Swedish;)
After four years in Sweden you would be granted a permanent residence, and one year later you could apply for Swedish passport.
The requirement of 'degree in computer science' is just a part of standard job description, at least I was never asked about my (missing) degree.
One interesting option to consider are 'consultant agencies'. They hire you on a permanent basis (often offering relocation) and then offer you to companies. This way you may reach companies not offering relocation themselves (e.g. startups). A small consultancy I am working for now, Go See Talents [2], is offering relocation from outside EU (along with mentoring for less experienced developers, which is probably not the case for you)