We will be disembarking from a cruise at 6:15am would it be possible to catch a train to La Spezia at 7:45am or does the unloading of the boat take longer? Trying to catch a train that is only 3 hours not the 4.5 nor don’t want to sit around until 1pm with the next speed train.
Is this something you could ask your cruise line or you might try one of the cruise forums.
When exactly are you traveling, and where are you looking at fares? There is an Intercity that leaves at 10:47 that takes slightly over 3 hours, if you don't make the 7:45.
If the ship was on time, and you self disembarked and walked out of the port via the South gate this is theoretically possible.
However the stress level is high. The ship could be delayed at Sea for very many reasons. You would have to take your own bags off and as I say walk (as you ARE allowed to do). If all the stars aligned you should have about 20 minutes in hand.
You do not have time to wait for the shuttle bus. If you wait for the ship to handle your luggage even the 1047 is in doubt, especially if you also use the shuttle bus out of port.
If I was buying tickets at the station on the day I might just risk the early train. If buying ahead it is far too high risk. In that case either the mid morning train or the lunchtime one.
Personally I would opt for the 1pm train and get off the ship in a relaxed manner. If I had spare time I would explore the under rated town of Civi a bit.