Alitalia is only recruiting ENAC (italian CAA) certified cabin crew and on a temporary basis (contracts that can or can not be renewed at the airline's discretion).
It is quite a long time since they had courses for N.C. (not certified) cabin crew. If you are looking to get an ENAC licence then I'd suggest you start with other airlines like for example Lauda Italy/Livingstone, Blue Panorama, Neos, and AirItaly (which is run by ex AirEurope management). VolareWeb was the first Italian LCC but I wouldn't wish anybody to get a job there...anyway just a personal thought...WindJet is another LCC but don't know much about them.
If you do not want to get a licence then the only option I can think of is EasyJet out of MXP. They fly on UK CAA contracts and rules.
I am not sure about the US passport though!!
Good luck
FBW