1. Head over to the Firebase console and log in with your Google account.
2. Click on "Add project" and follow the steps to create a new project.
3. Once your project is up and running, go to the "Authentication" section in the Firebase console.
4. Enable the sign-in methods you need for your app (like Email/Password, Google, etc.).

1. Log in to the Auth0 dashboard.
2. Go to the "Applications" tab and click on "Create Application".
3. Give your application a name and choose the "Single Page Web Applications" type.
4. Jot down the Client ID and Domain from the application settings, you'll need these later.

1. In the Auth0 dashboard, go to "Connections" > "Social" and pick the social providers you want to use (like Google, Facebook).
2. Enable the chosen social providers and set them up by following the provided documentation and adding the necessary keys and secrets.
3. Head to the "Rules" section in the Auth0 dashboard and create a new rule to map Auth0 user data to Firebase user profiles, using this template as a guide:

function (user, context, callback) {
  var firebase = require('firebase');
  firebase.initializeApp({
    databaseURL: 'https://<your-firebase-database>.firebaseio.com',
    serviceAccount: {
      projectId: '<your-firebase-project-id>',
      clientEmail: 'firebase-adminsdk-xxxxx@<your-firebase-project-id>.iam.gserviceaccount.com',
      privateKey: '-----BEGIN PRIVATE KEY-----\n<your-private-key>\n-----END PRIVATE KEY-----\n'
    }
  });

  if (!user.app_metadata.is_integrated_with_firebase) {
    // Your custom logic to map Auth0 user to Firebase
    firebase.auth().createUser({
      uid: user.user_id,
      email: user.email
    }).then((userRecord) => {
      console.log('Successfully created new user:', userRecord.uid);
    }).catch((error) => {
      console.log('Error creating new user:', error);
    });

    user.app_metadata.is_integrated_with_firebase = true;
    auth0.users.updateAppMetadata(user.user_id, user.app_metadata);
  }

  callback(null, user, context);
}

1. Go to the Firebase console and navigate to "Authentication" > "Sign-in method".
2. Choose "Anonymous" as a sign-in provider if you plan to handle anonymous authentication in your app.
3. Add a new OAuth provider by clicking on "Add provider" and selecting "Custom".
4. Enter the Domain and Client ID from Auth0.

1. Install Firebase and Auth0 libraries in your application:

npm install firebase @auth0/auth0-spa-js

1. Initialize Firebase in your application:

import firebase from 'firebase/app';
import 'firebase/auth';

const firebaseConfig = {
  apiKey: '<YOUR_API_KEY>',
  authDomain: '<YOUR_PROJECT_ID>.firebaseapp.com',
  projectId: '<YOUR_PROJECT_ID>',
  storageBucket: '<YOUR_PROJECT_ID>.appspot.com',
  messagingSenderId: '<YOUR_MESSAGING_SENDER_ID>',
  appId: '<YOUR_APP_ID>'
};

firebase.initializeApp(firebaseConfig);

1. Initialize Auth0 in your application:

import createAuth0Client from '@auth0/auth0-spa-js';

const auth0Client = await createAuth0Client({
  domain: '<YOUR_AUTH0_DOMAIN>',
  client_id: '<YOUR_AUTH0_CLIENT_ID>'
});

1. Implement the authentication logic to sign in with Auth0 and then sign in with Firebase using a custom token:

async function handleAuth() {
  const auth0User = await auth0Client.getUser();
  const idToken = await auth0Client.getIdTokenClaims();

  const firebaseUser = await firebase.auth().signInWithCustomToken(idToken.__raw);
  console.log('Firebase User:', firebaseUser);
}

1. Use the handleAuth function in your application to authenticate users:

<button onclick="handleAuth()">Login</button>

1. Run your application and click the login button.
2. Follow the Auth0 sign-in process.
3. Check in the Firebase console to see if the user has been successfully authenticated and added.