If speed is really your concern you'll need to get creative and search buses and different train/bus combinations.
It looks like several companies run long distance buses in the area. Busmiccolis run buses from Matera to Naples twice a day (middle of March) that take 4 hours and are about 18e.
https://www.busmiccolis.it/en/
You would need to then cross to the Naples train station and take the Circumvesuviana to Sorrento.
There are other companies check out this site for more options: https://www.materaturismo.it/en/how-to-get-to-matera/
If you want to really play around it looks like Busmiccolis runs a bus to Pompei near the Trenitalia bus station. You would need to cab to the Circumvesuviana station and then ride to Sorrento. There are other non-Naples destinations for buses but this probably gets you closest from what I could see. Would it actually be faster trying Pompei or other destinations? Maybe, but it will involve more moving parts.
The closest I can see by train/bus combo is taking the train from Naples to Ferrandina which is about 30 minutes driving from Matera.
There are a couple of direct trains a day that take about 3 hours or so but you would then need to coordinate with the Matera > Ferrandina transportation. There are several bus companies that run that route but it would be a matter of getting there and then aligning that timing with the train.
Honestly the bus is probably the fastest, fewest issues and cheapest way to go.
Good luck,
=Tod