[bberkgaut]

It's exactly like @rasjani & @piva00 put it.

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).