What languages do you speak?

Nobody hires you because of whatever you are running away from.

If you get hired, it is because of 1. what skills and experiences you bring with you, 2. how well these fit to the open position, and 3. how much of it you can prove (should be 100% - you better don't claim it if you can't prove it).

One very, very, veryvery important "extra question" is the language skill. It is not because we Europeans would emphasize language, but because the language skills are missing so often with immigrants.

Read up on the blue card if you qualify for it.

Then, maybe check EURes

You need to be much more specific. You need to say what your exact job will be and have a solid reason as to why the European company couldn't hire a European to do it. This isn't a choice thing, this is a legal requirement to get a work visa. You need a real qualification.

You could also consider working an american job remotely in Europe

Are you looking for just any job? Then it will be difficult.

Are you specialized in some way? Then you might have better chances. But as someone else said, the company would need a reason to hire you instead of someone just around the corner.

Companies tend to outsource jobs to cheaper countries, so unless you got some super special rare skills that can't be found anywhere in Europe or you want to compete with Indians for a crap hotline job, I'm afraid you''re out of luck. Also as far as I know (this might be outdated information though) as an US citizen you're required to pay income tax in the US no matter where in there world you're working, meaning you'd be paying income tax twice, in the EU and the US.

From the experience of a friend of mine: if you are of European descent, try finding out about your lineage and if that can somehow get you a European citizenship.

A friend of mine, who is Mexican, wanted to remain in Germany after finishing her Master's degree, since she had a German boyfriend and generally believed her prospects were better here. While it's possible for non EU citizens to get a work visa, the requirements are very high. She ended up applying for Spanish citizenship, since one of her grandparents had emigrated from Spain. After getting the Spanish EU citizenship, everything was a breeze. She didn't need any further paperwork, could remain in Germany indefinitely and apply for any job that doesn't specifically require German citizenship (such as some public service jobs).

Similarly another friend of mine, who is Brazilian, now holds German citizenship, despite not speaking a single word of German. He's fluent in French though and has found work in Luxembourg easily.

Therefore, if at all possible, try getting any EU citizenship via your grandparents/great grandparents. It will open the door to living and working in any EU country without ever needing a visa or work permit.

Do you enjoy dark and cold weather?

https://www.thelocal.se/20201103/how-americans-can-move-to-sweden-usa-permit

Firstly, you should think about the area you want to move to. Accordingly, you may need to learn languages. In the UK, the Nordic countries and Germany, you can get by well with English. In France, however, French is usually a must.

There are a few US-Americans working here in Luxembourg (mainly in banking and IT). English is often sufficient for professional purposes here. Privately, at least one other language is important (French, German or Luxembourgish). In a public school, children learn all three languages. There are a number of immigrants here who no longer understand their children.

All in all, it is still possible. Take a look around the job portals and simply apply.

Are you moving to Europe or trying to find a job in Europe while living in the US?

I think moving to Europe is really the only option unless the EU company has a US entity.