How can a US SW engineer to get a working visa in Europe?

First get a job offer an interview. If you are senior enough, a recruiting agency can get you connected in no time.

Heads-up: salary for very senior software developers in Europe are between half and one-third of what they are in USA.

In Germany it's pretty straightforward. If you have a job offer as a software engineer, have a related degree and earn over a threshold which most experienced candidates will meet, you automatically get a so called "Blue Card" work visa which has some benefits over a normal work visa. If you lack a related degree or don't meet the salary threshold you have to get a normal work visa which requires evidence that no suitable EU citizen was available to take the job, but this is highly likely to be approved.

There are no quotas or waiting lists, and you do not have to be "sponsored".

I have a European passport so after more than a decade working at FAANGs, I moved to Germany from SV and set up my own business. I've also lived for a few months in a number of different European countries.

Based on my own experiences, I'd say it makes little to no financial sense to move to Europe from the US, if you're going to work for somebody else while leaving a top-tier SV compensation package behind. Salaries are a lot lower, and taxation in rich EU countries is generally very high, you're looking at 40%+ effective tax rate.

In addition to that, a number of EU countries have painful wealth taxes. The Netherlands doesn't have a wealth tax per se, but it has a preposterous across the board tax based on an "assumed 4% return on the entirety of one's savings+investments". As someone with multi-million dollar investments in the US, this swiftly caused me to abandon Amsterdam as a potential base of operations.

Depending on your financial situation you can also get 'gold' visas.

- 500K worth of real estate investment in Portugal gets you EU permanent residence.

- 750k investment in Malta gets you full out EU citizenship.

After this you are fully entitled to live/work/receive healthcare anywhere in Europe with no strings attached to an employer.

Controversial I know but the option is there.

As far as the UK is concerned, it is possible to get skilled work visas for tech jobs in the UK. The company needs to be willing to sponsor you, and some other criteria need to be met. You can get permanent residency after 5 years. Other routes are available depending on your background (if your grandparents were British for instance this is very easy), or if you’re young and interested in studying, degrees now lead to graduate visas.

You will likely be taking a pay cut, but you might have a higher standard of living depending on how much you currently make. You will also almost certainly get better holidays (5-6 weeks is fairly normal).

See https://www.gov.uk/skilled-worker-visa for more details

In the Netherlands, you can get a job offer and the company will sponsor a highly-skilled migrant visa, which lasts for five years and can be renewed. In addition, the government offers a tax break of 30% for skilled workers from outside the country for five years.

If you have European ancestry you may quality for citizenship (check back at least three generations).

If you were born in Ibero-America (former Spanish and Portugese colonies including Puerto Rico) you can gain citizenship of Spain with two years of residence.

In the Netherlands, companies can sponsor a software engineer for a work visa as a highly-skilled immigrant. In Germany, a software engineer can easily get a blue card, which gives someone the right to work and live there.

In both of these countries, the first step is to get a job offer from a company and go from there.

The Global Talent visa is the best path for the UK: https://www.gov.uk/global-talent-digital-technology

A quick seach brings this up https://www.schengenvisainfo.com/working-schengen-visa/

I would think it’s a function of the job offer, seniority and the “help” of the hiring company. That, plus the passage of time. The more senior the candidate is (and can prove), the more varied the visa possibilities are. Each country has various visa description pages on line somewhere and there might be eu level stuff as well (never looked). But it’s non trivial unless there’s a real skill match as, technically, they might have to guarantee there’s no natives who can do the work.

Check whether there are specific country-level agreements like nafta between us/Canada and Mexico. This changes the rules for the appropriate countries’s citizens. Canada/us is quite straightforward to cross if a job offer is in hand and one of a fair number of career categories is met.

Interested in this as well. Is it any different if you've got a remote job for a US company (I've got confirmation they'd let me move over to contractor status).

I don't have an answer for you at the moment, but a number of my US SW engineer friends have moved to Berlin on some sort of work visa.

A couple have been there for years, at this point.

Come to Greece, Chania, and if you are into SW engineering then lets talk :)