Train from Florence to Sorrento

Use the official train site
RailEurope is a third party reseller that won’t sell all available trains and charges a fee

https://www.trenitalia.com/content/tcom/en.html

Their app is easy to use as well

There are fast trains to Napoli Centrale
(From Firenze SM Novella)
From there you take a commuter train Circumvesuviana to Sorrento- no need to book in advance

https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

Is Sorrento your final destination?

Yes, Sorrento is final destination. I've now found it on Trenitalia site which is hard to use.

If you do a search for “Sorrento” here on forum you’ll find lots of info
There is also the tourist train Campania Express which runs on same tracks and can be booked in advance
It only runs a few times a day
Info in the Sorrento Insider link I posted above

Here’s one thread
https://community.ricksteves.com/travel-forum/italy/travel-between-sorrento-and-naples

I think you'd have to catch the fast train through Rome to Naples. And then get on a local train that takes you back to Pompeii, Sorrento and the Amalfi Coast area.

There are a couple direct from Florence to Naples that don’t require a change in Rome

Between 8:48 and 20:14 Trenitalia runs 23 direct trains (i.e. no need to change in Rome) from Firenze SM Novella to Napoli Centrale.

Italotreno runs its own 14 direct high speed trains between the same stations.

Since both companies want to break-even, all these trains stop at Rome's main stations, Tiburtina and/or Termini. It's a stop, passengers going to Naples do not need to transfer to another train.

Jamie if you find hard to use Italian station names on official sites, remember that you won't see Naples or Florence written anywhere in Italy.

Even bilingual monitors use Italian names. You'd better get used to them now.

Look at the Website Rome to Rio you plug in where you want to go and he will provide multiple solutions including trains.
When using the Trenitalia website, as someone mentioned get familiar with all the actual Italian names of each city, then the actual name of the train station (search on the forum for that) on the top for your search criteria make sure you have 00:00 as your time to ensure all the solutions pop up. Just like with anything new, it seems "hard" at first but once you start playing around with it, it is actually very easy and the Kiosk screens at the train stations look exactly the same, so it is useful to get familiar with it. Take it from someone who has never used a train or subway before traveling to Europe, I was intimidated for sure, but the forums and Rome to Rio really really help. Another Website you can checkout is "The Man in Seat 61" who is exclusively train travel and also YouTube, just plus in "Florence to Sorrento" and I am sure you will find a traveler who has documented how to do it by train. And remember the research is just as fun as the traveling.

Raileurope is the worst of the resellers; Steve's referring unsuspecting people is despicable.

We used RailEurope. It lets you put multiple trains in your cart which we were not able to do using DB (Germany) train site. So worth it to us to pay the fee.