You can buy secondhand servers in loads of places with cash purchases. The boys on /r/datahoarder do it all the time. This isn't rocket science, but perhaps I'm overestimating the type of people who would would run a service like Parler.

Don't they get most of their hardware off eBay these days? (Not that I'm incredibly familiar with that space - I'm more interested in serious redundancy for small important files.)

Anyway, the government has plenty of experience handling terrorists dealing in cash. It doesn't need to be perfect.