I flew FCO-PHL in 2016 and we arrived at the airport a bit after 7 AM. We waited in line (first in "Priority") before they let us in to the departure counter area at 7:30. At that time of day there was absolutely no line for security nor for exit immigration. The whole process of checking in, checking bags, security, immigration, and the shuttle over to the terminal took <15 minutes.

Don't worry at all, but I would be there no later than 7:30 AM, maybe 7:15.