Marriage Sponsorship - International Student

I (a US citizen) have been with my partner (an international student) for almost three years. She has already completed a Master’s last year and started a PhD 10 months ago. We have talked about getting married but wanted to wait until I was done with my PhD (I am starting my third year). She is completely miserable and is plans to quit her PhD. She has explored every opportunity of either switching programs and finding new advisors before choosing to quit her graduate program but nothing has panned out and her mental health cannot handle that anymore.

I would like to marry her ASAP so she doesn’t have to leave however, she will quit her grad program before we can get a green card. From my understanding she has 15 days to leave the country after she quits. The other wrench in the problem is that we are currently long distance (500 miles) as we study in different states. However, I am not worried about proving how real our relationship is- we have pictures together dating back to 2021 and trips we’ve taken and visits back and forth.

If we get married and she quits her program before everything with her green card is finalized, will she still have to leave? Can she start working immediately after we get married? What documents do we need so she can get a job? If we don’t file for a green card immediately does she have to leave? I am also worried about the cost of a green card which is why I don’t want to file immediately… but if that’s what it takes, I will do it.

Thank you in advance for all the advice and support!