I'm not sure that you have to have a Green Card. If you can find a company that really needs your expertise then I think an L1 visa will suffice. (That is what I had when I flew DC-10s for a Part 121 operator out of JFK for over 3 years).
I think you need to think carefully about money.
The days of US airlines paying megabucks to pilots are over and the bucks that you can get are "two to the pound". Unless you are 16 years old you are unlikely to earn a decent seniority and salary with a US operator for a very long time.
One of my old F/Os is a trainer with NWA and his pension fund, salary and every other facet of his dedication to the company has all but disappeared.
Find another occupation in the USA and fly for fun. The money is cr*p.