This is an hour and itinerary that's probably best served by taxi. It should cost €15-€20.

There are certainly public transport alternatives, but they are messy and time consuming. The metro opens at 05:30-ish, and you'd need an early start as you have to change at Omonia to get on the Piraeus (green) line.

There's a 24H bus service from Syntagma. The tram from the Intercontinental to Syntagma should be working by 05:30 - but you'd need to check.

Whatever means of transport you use, make sure you know exactly where - which "gate" - your ferry leaves from.