I had a similar problem with my Alfa. Did a little research and found it was a bad relay. Common issue with the Guilia.
Probably not related, but my Testarossa did something similar after sitting for a few months. I just cleaned and tightened all the grounds and the positive leads which went to the starter. Fine now.
Yep - all of the recent posts are on the money, it's electrical 100%. It could be a wide array depending on complexities of theft deterrent, ignition switch, relays, solenoids and grounds. Depending on how far you're willing to go my next step would be to get an assistant, put a meter on the items downstream of the key and see where you get power and when. I'd start at the starter solenoid, probe power going in and then power on the backside at the starter. I'm betting it's there. Other smarter folks may have better testing ideas, but my simple brain says try that.