I'm assuming that based on your username, you are an EU citizen? If so, apply for a job with any large US based company in one of their European offices. For example, Google in Zurich or Dublin, Amazon in London, etc.

After one year, you qualify for what's called an L1B 'internal transfer' visa. You can then transfer to another team within the same company that's based in the US. In many cases the company will sponsor your visa application and even the cost of moving (e.g. plain ticket, cost of shipping your belongings, etc.)

Once in the US, you can start the application process for a green card. As long as you're not a citizen of either India or China, this should take 2-3 years.

I'm Dutch and this is the path I took.