In a hypothetical situation where you get a law passed in your country, where it's mandatory to perform age verification on all social media apps, it's simple.

No verification? Jail time. Will they go after you? They could, if someone pointed them towards your server. (I think they even have to, at least in our country, the government has to persecute a crime they are made aware of if I remember my college law courses right)

In some states, if I understand it right (based on a quick googling, might be false) failing to do verification for porn can be considered as a felony. It's a slightly different example (porn vs. social networks), but if the laws are written in the same way, there's not really much you can do about it.

Completely anonymous hosting that's in no way tied to you (through IP, credit card, location, domain, logs, etc) is difficult. While you'd still probably be fine if you have a private-use server, you'd still give anyone who doesn't like you and knows about it a pretty easy way how to make your life a lot more difficult. This of course heavily depends on how would (will) the laws be written in your country, but give the track record of lawmakers understanding tech, there is a chance that even small self-hosted stuff would catch flak. If it's written in such a way to not be i.e limited by user count, then there's not much you can do.

A lawyer would probably be able to talk you out of it, but you'd still be charged and it would suck (and be expensive) to deal with.

So, yeah. "How could the government force me to enable it" boils down to "jail time". I mean, it's basically a similar question like "how could the government stop me from using Telegram or VPNs", and IIRC there are some examples for that already.

EDIT: Not having public sign-up enabled could be a way around it, since random people can't make an account there, so you're basically doing age-verification by a veto. However, if someone under-age got into your server, they then have a leverage on you, since they are there illegally (in the hypothetical scenario).