Civitavecchia Cruise Port to Rome and back in a day

This is totally unrealistic.

Even if the all aboard time is 30 minutes before departure (and NCL are known to now be requiring an hour) you can't afford the 6.02 pm train to be even slightly late. The 6.47 train you can sprint all you like but you have missed the ship. By the time you get to the station the gangway has been raised. By the time you are at the ship it has cast off.

Likewise the morning requires the ship to be exactly on time. If there has been anything happened at sea or even the port pilot is slightly late you are in trouble. There isnt an airbridge, a manual gangway has to be set up and the ship cleared by the port authorities. Just setting up gangways takes time. Time you haven't got. Getting off the ship at 7.15 is distinctly optimistic. If you do so the 7.44 is very, very tight. I wouldnt even place bets on you catching the 7.58 train.
The regional trains are not known for their high punctuality, and this is peak commuter time.

Does your cruise ship offer an excursion into Rome?
That is the safest option

We faced a similar dilemma and opted for the Rome excursion offered by our ship. They then are responsible for getting you back on time and I believe will hold the ship for you if your group is late. Big benefit of the ship excursions. Be warned - it’s a long and exhausting day!

I am not a fan of ship sponsored excursions but agree that, in this case, taking one is your best bet. What you propose just sounds like such a "stress fest" that it would undermine any enjoyment of your day in Rome. You don't say if you have been to Rome previously? If you are familiar with the city you might see if the ship offers a "Rome on Your Own" excursion where they just provide transportation both ways and you explore sights on your own. Otherwise I think Rome is fairly overwhelming and you would do best to book a ship's excursion.

No way can you do this. Totally unrealistic. You should either buy the shore excursion or just travel to Rome with no timetable, walk around enjoying whatever you see.

Thank you everyone for the reality check. We have deviated to a Vatican only tour that includes the basilica at 1:15 to 4:45. This puts us at the train station at 5 and if on the train by 530 back to the ship by 7, which is an hour before disembark. The morning we will just take the train as early as we can and I have mapped out a self walking tour from Roma termini to colusseum, forum, trevi fountain and ending st the Vatican. About 4 miles not bad. At least with this we can deviate as needed.

Hate to be Debbie Downer, but looking at your revised plan, all I can say is "Good luck". We've taken the train from the port to Rome and back several times, and there just isn't anyway I'd try it a the risk of literally missing the boat. A ship excursion will cost more than doing something on your own, but not nearly as much as getting yourselves to the next port if things go wrong. Just offering food for thought.

You’re at risk of missing the boat with this schedule. Scrap the Vatican and fixed time tours so you can relax and savor your day in Rome.

I like the revised plan. If you have any reason to worry about the train not getting you to the boat in time, you can take a taxi. Your walking tour may end up being changed up, so prioritize your must see items. For me that would include the Pantheon, the Spanish Steps and gelato.

I do hope you'll come back and let us know what you did in the end and how it worked out. 2025 being a Jubilee year is the least of your concerns. Honestly, you lost me at "the ship is due to dock at 0645. With proper planning, I am estimating being off the ship by 0715". Even if it does dock at 0645, the crew's ability to lower the gangplank and get you and the other 3000+ people looking to get off to be on your way at 0715 is unrealistic. Rest assured that things just will deteriorate from there. Others are offering good ideas here. Take a ship's excursion. (Not the first choice of many, but you do get the privilege of exiting earlier than the masses, a less stressful commute, someone leading you around who knows the neighborhood, and, if you stay with the group, the guarantee that the ship won't leave without you.) Go into the city with no pre-booked tours. Choose less congested (ha!) tourist sites to visit. Walk around and eat gelato. All better ideas that the plans you have outlined. Good luck!