Hello @S and welcome to our community!
Both of you need to hand in a valid ID or passport at the Italian registry office along with a birth certificate, a certificate of no impediment and maybe some other documents too. Get in contact with the civil registrar (“ufficiale di stato civile”) where you want to get married to find out what documents exactly you need. You can also ask them about the duration of the whole procedure. They will be able to give you the most exact information.
We had a similar question here on the website recently. Please check out the information provided here: https://www.wefugees.de/k/questions/2357
Unfortunately I can’t tell you whether your documents will be sufficient to prove that you are single or not. Once again it probably makes sense to just ask the civil registrar and explain the dilemma you are facing. Or Maybe @Marcel or @Steven have an idea on how to tackle the issue.