How to get JWT Token through passwordless signin link

Question

We (company A) are developing an App. We want to expose functionality of Company B in our App (Post / Get calls to their API).

Requirements:

• Company B wants us to provide a solution that costs them minimal setup time from their end.
• Legally we cannot show a username and password field in our own App to authenticate the user with Company B's API.
• We could ask the e-mail address of the user with a submit button and trigger a password-less flow? But open to better suggestions.

Flow of Company B's App:

• Show login page

• POST call with username and password: https://identitytoolkit.googleapis.com/v1/accounts:signInWithPassword?key=AIz..4E

• Response call with JWT Token:

    https://identitytoolkit.googleapis.com/v1/accounts:lookup?key=AI..4E
  
    Body:
    {
       "idToken": "eyJhbGciOiJSUz...KFQ"
    }
  

Pasting this JWT Token in our API calls to Company B is enough for this to work.

Question:

Would a password-less flow work? And if yes, how would I get the JWT Token?

Things tried:

• Tried this tutorial but it also refers to a firebase object, and I don't think users are stored on firebase.
• Tried the firebase email-link signin tutorial. They have their userbase on google Identity, and not on Firebase. Otherwise this would be a great implementation.
• Zapier connects to all these thirdparty api's by actually using and storing the user's information. This would be the easiest, but not possible for us.