Just pull out that old Nokia phone that has no camera or internet or anything, and buy a sim card from a supermarket or something, and do your thing.
Though, if you use the sim card, and if the government really wants to catch you, they probably can. Like, pinging off of towers or whatever, and getting your exact location, or at least an area where you're at.
I don't much care about that though, so I have a few sim cards that I use like that, for verifying twitter accounts and paypal and stuff like that.
One advice. In my country we have a few operators that offer these sim cards. And they have different rules over how long the card lasts for if you don't load credits. So one company is 3 months, another is 6 months, another is 12 months. So your credit expires for example after 2 months, but the card continues to work for another 3/6/12 months. In this period you can receive calls and messages, but your credit has expired, so you can't call anyone or send a message.
So I only use the cards from the provider that lasts for 12 months, so I only have to load credit on each card once per year, and that extends the life of the card for another 12 months. And since I only need these sim cards once in a blue moon, if twitter or paypal or whoever wants me to verify my identity, this works perfectly for me.
Note, if the 12 months pass and you don't load any credits on the card, then the card expires, and the only way to get it reactivated and get the same number is to go to the company and ask for it. But then you have to give out your information and register the card in your name. So if anonymity is a thing, keep that in mind.