She might be able to. As you know, there are many exceptions for Cubans and a non-Cuban spouse may be able to adjust status and the same time as the Cuban. The first step is certainly to get married. Then, once you've been here for a year, you can file for adjustment of status. The Miami USCIS office sees many Cuban Adjustment Act cases, but you may still want to talk with an immigration attorney to make sure everything goes smoothly with both of your cases.
This general advice does not create an attorney-client relationship. If you are interested in discussing this situation further, call 678-713-4255 for a consultation.
Generally speaking, if you obtain your residence through the Cuban Adjustment Act, your spouse, even if not Cuban, can also obtain residence through the CAA so long as you are residing in marital union. The location and timing of your marriage is not necessarily important. Consult with an experienced immigration attorney who advice how best to proceed given the facts of your case.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.
Just a quick question - you indicated your "partner" and I am just curious as to whether you mean a same-sex partner? If that is the case, even if you marry your partner in the USA in a state that recognizes same-sex marriages, he/she will not be able to apply for a green card under Cuban Adjustment Act unless and until USA Immigration laws recognize those marriages/relationships (which I think will eventually happen, but not in the time that you need it to). Just a FYI and please ignore me if that is not your situation. Best of luck to you both.
Assuming you are eligible for Adjustment of status under the Cuban Adjustment Act, then your lawful wife would be eligible to apply for Adjustment of status under the Cuban Adjustment
Act so long as she was lawfully inspected and admitted to the U.S. and resides with you. You should retain an experienced immigration lawyer to assist you in the process since the validity of the marriage must be very well documented.