The key phrase that you’re looking for is “TOTP” (Time-Based One-time Password) – and it is a specification, rather than an API maintained by Google.
At a very high level, your backend will generate a secret that it will share with your users’ Google Authenticator app. At login, both the Authenticator app and your backend with use the stored secret and current time to generate a single-use key. If the keys match, it means that the secrets match, and the user may be logged in.
The SpeakEasy node implementation seems to be pretty popular on github.