We dock in Livorno at 7am. Any chance we make it to the train station to catch either one of the trains that run between 8 and 8.30. I believe with the no walking in the port and hard to come by taxis and the shuttle etc etc it's 45 minutes to the station!
If you can get a taxi it is only about 10 min to the station. We have often made the 8 am train. The trick is to be one of the first off the ship and than head straight to the taxi cue. There is usually an Italian man who tries to organize all the taxi trips and just make it clear you need to get to the station (stazione) fast.