flyingturco,
I'll say that for a young expat looking to come to the US and establish a flying career, you've already got three
HUGE hurdles jumped: Green Card, a job offer from an airline in Turkey giving you experience in a large airplane and a 4-year degree. You're way ahead of the game.
I assume since you said you don't have FAA licenses that your university aviation degree was not gained in the USA ? If so, IIUC, you'll need 1,500 hours total time to qualify for an unrestricted FAA ATPL. Those who qualify for a (restricted)ATPL with sub-1500 hour flight times are graduates of one of a number of FAA-approved US universities:
https://www.faa.gov/pilots/training/...ority_List.pdf
If you've got a job waiting at Turkish, that should quickly get you experience to 1,500 hours.
Perhaps havick or zondaracer will come along and offer an opinion about the likelihood of a US regional taking you onboard with your non-US licenses and getting you an unrestricted FAA ATPL via their in-house training program as they now do for the Aussies they hire. If that were possible/probable, it would save you lots of time, money and aggravation.
Good luck with your journey.