Family Visa for Students (Rome)

Hello - My husband will be starting his MBA at LUISS in November, and I am looking for some help on obtaining the family visa. From what I understand, I cannot get my visa until he has applied and received his residency permit. We are both currently living in the US and plan to move together. I am concerned about the length of time typically required to get the permit and my ability to remain in the country legally. If you have gone through the process, I would love your advice. We have reached out to the university but they cannot apply for the Nulla Osta Per Motivi Familiari on our behalf to expedite the process.
Thanks!
Sara