On the Firebase documentation, it states that the web API key will be auto-generated when:
Firebase will automatically create a new web API key for your project when you do any of the following:
- Create a Firebase project > Browser key auto-created.
- Create a Firebase> iOS App > iOS key auto-created.
- Create a Firebase Android App > Android > key auto-created.
I have tried creating a new Firebase project as stated, but the web API key is not being generated.
UPDATE: The answer to the question is in the comments. ("It gets generated once you go into the "Authentication" section for the first time")