What is the best way to get a throwaway phone number to try this? Is it possible to get one online?

You can get a prepaid eSIM online, depending on your country. It's cheap and you don't have a monthly fee

I've used textverified in the past, maybe you could check it out (small cost per verification)

In most of the EU dictatorships, there's no legal way to obtain a phone number without registering with your real identity.