It is impossible to wake up on the Amalfi Coast and fly out of Rome the same day. Since Sorrento is not as far as the AC, it is simply "unwise" to wake up in Sorrento and fly out of Rome the same day. You are playing with fire.
https://search.ricksteves.com/?button=&filter=Travel+Forum&query=Sorrento+to+FCO&utf8=%E2%9C%93
It's not entirely fair to read between the lines, but it appears that you don't have much European travel experience, or public transportation experience. I mean, for example, that you should have, by now, gone to https://www.trenitalia.com/en/frecce/frecciarossa.html , clicked on the English button, and started to explore the connections between Rome and Sorrento. Have you learned how to get between FCO and the downtown Rome train stations?
https://search.ricksteves.com/?button=&date_range=2y&filter=Travel+Forum&query=frecciarossa+naples&utf8=%E2%9C%93
Please don't think I'm yelling at you. If you are arranging your own travel, i.e. not using a bricks, mortar, and flesh Travel Agent, you MUST learn to do these things. You cannot plan a multi $1,000 trip using only advice from a newsboard. (I mean, for example, if you miss your fast (Frecciarossa) train from Rome, you need to know that you cannot use a reduced-fare ticket on the next train. You have to learn about the various fares, and their flexibilities, just like you do about your air tickets.
Even more important, you have to learn that the train you get on in Rome cannot go all the way to Sorrento. You have to weigh the cost of the four or five ways to get from Naples to Sorrento, against the time and comfort issues.
https://search.ricksteves.com/?button=&date_range=2y&filter=Travel+Forum&query=Rome+to+Sorrento&utf8=%E2%9C%93
Our host has some excellent free travel tips, top left:
https://www.ricksteves.com/travel-tips
https://www.ricksteves.com/watch-read-listen/read/articles/naples-sorrento-and-the-amalfi-coast