That looks like the only direct train from Monterosso to Naples and departs at 5:28 am. You could save about 1 hour, by getting off that train at Pisa and changing to a Frecciabianca to Rome, then changing to a Frecciarosso to Naples. That is about the fastest way. Costs a little more, so it is up to you. There is no food service on the IC train, so be sure to pack snacks and drinks for the trip.
Most of the time saved on the 2 change route is because the Frecciarosso uses dedicated high speed tracks between Rome and Naples. The IC train does not stop at Rome Termini, but at Rome Ostiense.
I see from your other thread that this trip is planned for September 2023. There could be significant schedule changes between now and then, so take another look this next year.