> Is there a way to get a disposable number that cannot be tied to your identity somehow (in the US, at least)?

I have never had to present id when buying a prepaid phone in the US.

Approach a stranger who needs money, somewhere well out of view of any cameras. Pay them to buy a prepaid phone from Walmart or the like, using cash, on your behalf.

You can buy accounts on the /r/BitMarket subreddit.

That arguably != "cannot". But you can get close by using Tor via nested VPNs to access Reddit. And by paying with some suitably anonymous cryptocurrency. Maybe well-mixed Bitcoin. Or some Etherium flavor, perhaps exchanged to Bitcoin.

Alternatively, some virtual SMS sites may still work for Twitter. Or there are sites where you can lease actual hosted SIM cards.

In Russia you can pay several roubles (which you can deposit using bitcoin) to a service providing phone numbers for registration. Such services are usually used by spammers (sorry, I mean marketers and SMM people) to create multiple accounts on social networks, but can be used to protect one's privacy too.

Sadly, not all services are good. Many of them block SMS from banks, loan firms and payment systems and I don't want to support them.

There are countries that allow you to buy SIM cards without identification, even in bulk. (e.g. Ukraine) They are also sold on various platforms including reddit. You can even enumerate known ports for certain web interfaces (cough ACE *cough) and access them with default passwords.