Forget about a greencard. Even if you marry an American citizen, it'll still take you a long time to obtain it.
It's not like you're trying to find an airline that may sponsor you, it doesn't happen that way, yet.
Way too many regulations from TSA working against you and that's JUST to obtain your type rating for a 121 jet in US. Forget about actually flying it...
Even as a green card holder, it can be a PITA just to go through recurrent and getting the ok to sit in the box for 4 hours, especially if you have to reschedule it. It costs the company money too to get the authorization for your sim check.
Unless you have a greencard already, I would channel my time and energy elsewhere to seek employment.
Just my .02 cents.