There are 2 parts to using Fireabse, the client SDK and the admin SDK.
The client SDK is what's loaded in the front end and used for 95% of use cases like what u/whstl mentions.
The adminSDK can't be used in the browser. It's server only and is what you can use inside a custom REST API. In your use case, the email verification loop has to happen on a backend somewhere. That backend could be a simple AWS lambda that only spins up when it gets such a verification request.
You're now using a hammer for the front end and a screw driver for the finer details.