Quoted: Allright, Sweden basically sucks.
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I've been saying that for years !!
You are correct that a H1B visa is "sponsored" by a company, and they need to be able to justify to the U.S. government that your particular skill is needed, and that there are not enough of them in the U.S. (in other words, they need to justify WHY they are hiring you over a U.S. citizen). Sometimes that can be pretty easy for a company, if they really want you - other times it can be a hassle, and a lot of smaller companies simply don't want to deal with it. So it CLEARLY helps to have a pretty unique or rare skill that is in demand in the U.S. job market.
So ideally, you would find a U.S. company that needs an electrical engineer with your particular skills and experience - and get them to offer you a job. They THEY will get the required visa for you.
The EASY way to get permission to live in the U.S. is to marry a U.S. woman.
That puts you on a "fast track" to getting permanent residency (also commonly called a "Green Card") which essentially allows you to work in the U.S. under the same terms as a U.S. citizen.