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Yes, you hold a job right now, but it is temporary job and temporary visa. To apply for GC through the employment, the job must be permanent. You are unlikely to call residency a permanent job. AMA has nothing to do with it.
However, your residency program can start advertising campaign while you are still a resident. But the formal application for Labor Certification (or I-140 NIW) can only be made when you become qualified for the job, i.e. the day after graduation at earliest.
You may want to consult immigration attorney. $200-worth consultation will bring you a clear understanding of the process, and fee may be waived if you retain that attorney to process your case.