It appears there are two posibilities for the train. Either early afternoon with an arrival in Innsbruck at 6:30 PM or to take the night train from Venice and arrive n Innsbruck at 4:30 am. I have two questions. Will they add an early morning run for the summer season and what do you do when you arrive in a city at 4:30 AM? Nothings open, which means do we just sit at the train station and find a place for breakfast at about 7:00?
A lot of the bakeries open at 6:00A so people going to work can grab a coffee and snack.
Take the day train. Night trains on the route are unreliable and filthy.
The first direct train departs at 13:34. However, if you are willing to make one connection (Verona), you can depart at 06:58, 08:58, or 11:03.
There are many reasons to take a day train, like the trip is not long enough for a night train and the scenery is worth seeing during the day, plus it costs less. But at least one of these trains is run by CNL, a Swiss chartered subsidiary of German Rail. I don't think you can characterize CNL as filthy and unreliable.
Thank you all for your input.