Not sure what you mean by "sourced through the employer".

Usually you need to have enough qualification and a job offer to apply for a work visa that is bound to the employing company for two years. Switching jobs requires reapplying. Afterwards, you can usually get a work visa that is not bound to a specific company, and less time limited.

Normally it's you applying for the visa, but in some cases the company hiring you can file the application, which can drastically reduce the time you have to wait, but cedes some control.

Of course, all this depends on your nationality and the country where you are applying.

For the HN crown I think you should consider skilled work-visa if you want to move, and I don't think it's unrealistic. You will probably need a job wherever you move anyway, this just means you need to find that job before you move. Without doxing myself completely, I know several North-Americans with that kind of visa here in Europe.

You need to apply for a position and get it. Then you need to apply for the visa. That can take a couple of months to process, which sounds like a lot, but remember that in many European countries this is on par with, or less than, the notice period for changing a job. So for the employer it won't make a big difference.

You will probably have to pay for moving yourself though.

What requirements? The only real requirement is to have someone sponsor you.

Everything else, including having passport and no previous history of war crimes, raping and pillaging for 5 years also applies to other visas anyway.

It's also not H1B type of slavery, there are not quotas, you can change employer whenever your want and not even lose fancy tax ruling. Work visa is the easiest way.

To be honest I think that Ancestry and Asylum are about as much "out of your direct control" as you can get, the latter especially (as in, unable to work, or leave that particular country, until the application is decided upon)

Remember that 'the EU' is around 30 individual countries each with their own work visa issuing procedures and rules - none of which are really at all comparable to the US system.

Seriously just choose a country and apply for a job with a company that doesn't explicitly state that they need you to already have the right to work in that country and see where it goes.