Is there any way for us to still apply for marriage?

While the requirements for actually becoming married are determined by the laws of the location where the marriage takes place, the requirements related to entry into the U.S. and becoming a Permanent Resident (getting a "Green Card") based upon the marriage are determined by U.S. federal immigration laws. Under U.S. immigration laws there is no requirement for a specific period of time for dating before a U.S. citizen may apply for a fianc?e visa to enable a foreign national to enter the U.S. for the purposes of becoming married within the required time, and then applying to adjust status to become a Permanent Resident. If you were to first become married overseas, note that there similarly is no requirement for a specific period of time for pre-marriage dating before eligibility for consular processing to enable the spouse to enter the U.S. and become a Permanent Resident. Of course, there are many other details that determine eligibility. There really is no substitute for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.

Much more information is needed. Where do you want to marry? Which of you is a U. S. citizen? Is one of you a lawful permanent resident? If so, how long has the permanent resident lived outside the U. S.? Marrying in Italy can delay processing for years in some situations. I strongly recommend an appointment or teleconference with a competent and experienced immigration attorney before there are more complications.