In theory, yes. In practice, if you'll try to avoid any interaction with sites affiliated with Google, Facebook or feeding surveillance data to them, you'll quickly discover that the internet became very small and much less usable than before. You don't need to use Facebook or search on Google to be tracked by them. Google owns one of the largest ad networks in existence, so if you visit any site that has ads or analytics trackers, the data about it will go to Google. Any site featuring Facebook social button may feed the data to Facebook. If you write to somebody with @gmail address Google knows about it. And so on, and so forth. For a highly technically skilled person, it
might be possible to avoid interactions with Big Tech while being able to still using modern technology, but it won't be easy. For a normal person without deep technical background it's pretty much hopeless unless they avoid using the internet entirely. Of course, using the internet is "voluntary", but this is a very weak consolation.
And, also, both Google and Facebook eagerly cooperate with state actors in censorship and other aspects - likely surveillance too. So there's not much difference in that aspect whether you work for the government directly or for somebody who takes marching orders from the government while being formally independent.