It varies per country, for example in the Netherlands as a software engineer and other "highly skilled" [1] roles you can get an HSM visa / work permit. I believe Germany, Denmark and others have similar programs.

This is how it works: you interview[2], get a job offer, sign it, then your employer applies for a work permit on your behalf. The only complicated part is collecting your own paperwork. You wait a few weeks/months for approval and move in. It's a lot easier than most people think. The permit is tied to your employment, though it can be transferred, but you cannot get a 'free employment' permit until after five years in the country.

For the EU as a whole, the Blue Card serves a similar purpose but is significantly more difficult to obtain.

[1] There is no skill/merit assessment like the USA, it's solely based on the salary threshold - basically delegates the skill assessment to the employer. Not every company has access to this program, the job must be advertised as including visa sponsorship.

[2] online. Flying over for a final round was common before COVID, I miss those days

+1

We hired someone from Syria as a small and newly formed company in Germany, and all we had to claim is that yes it is a high skill job above a certain salary threshold and no we cannot find a person available with the required skills in Europe. The visa application process from our side was simple and straightforward, no forms, no fees, just a short letter where they told us beforehand via phone what to write to get it accepted, and it was processed very quickly, a few weeks maybe. We didn’t even advertise the job before, it was a position/role created specifically for that person (so from that perspective there was truth behind the statement that we cannot find anyone else suitable for it.)