A "professional pilot program" at a university takes one year's worth of training and stretches it out to four years. At a premium price. And graduates often finish w/o a flight instructor certificate, so they have to complete that after graduation to get their first job.
Without an unrestricted right to work in the US you are not going to get a job. "I'm a pilot" is not a strong enough reason for a green card. There is no shortage of applicants for jobs.
You can certainly train in Europe and fly for an airline there.