Integration between Google sign in and Amazon Cognito

I have an issue in my react native application in the Continue with google flow i.e. Federated identity provide sign in, What I need to is if the user in not present in my Cognito user pool , This user shall be signed up in my user pool. If not, User shall be authenticated using its Gmail account.

What I have done so far Is used the following libraries

@react-native-google-sign-in/google-signin and amazon-cognito-identity-js and aws-sdk

I have created a webClientID , Android ClientID, IOSClientID and Configured OAuth Consent Screen and all the other setup needed from google cloud platform. I have enabled Social Providers and attribute mapping between google and Cognito I indeed get the ID token from google , but i get the following error

Error signing up user: [NotAuthorizedException: Client <client_Id> is configured with secret but SECRET_HASH was not received] which is related to missing client secret hash in the authentication request to Cognito after getting the Id token from google , and after investigation it seems that i need to create another App Client with client secret generation disabled in order to bypass this error

export const signInWithGoogle = async () => {
  try {
    await GoogleSignin.hasPlayServices();
    const userInfo = await GoogleSignin.signIn() as any;
    console.log("Google Sign-In Response for user-info:", userInfo);
    const tokens = await GoogleSignin.getTokens();
    console.log("Token :", tokens);
    if (!tokens.idToken) {
      throw new Error("Failed to retrieve Google ID token");
    }

    // ✅ Correct way to access email
    const email = userInfo?.data.user?.email || null;
    console.log("email :", email);
    if (!email) {
      throw new Error("Email not provided by Google Sign-In.");
    }

    console.log("✅ Extracted Email:", email);

    const userExists = await checkIfUserExists(email);

    if (userExists) {
      console.log("User exists, signing in...");
      await signInUser(email);
    } else {
      console.log("User does not exist, signing up...");
      await signUpUser(email);
    }

    await authenticateWithCognitoFederation(tokens.idToken);

    console.log("✅ Authentication successful! Redirecting to Home Page...");
    return tokens.idToken;

  } catch (error) {
    console.error("Google Sign-In Error:", error);
    return null;
  }
};

const authenticateWithCognitoFederation = async (idToken: string) => {

  const credentials = new AWS.CognitoIdentityCredentials(
    {

      IdentityPoolId: IDENTITY_POOL_ID,
      Logins: { "accounts.google.com": idToken },
    },
    { region: "<region>", }
  );

  AWS.config.credentials = credentials;

  await credentials.getPromise();
  console.log("✅ AWS Credentials obtained:", credentials);
};

const signUpUser = async (email: string): Promise<void> => {
  return new Promise((resolve, reject) => {
    const attributes = [new CognitoUserAttribute({ Name: "email", Value: email })];

    userPool.signUp(email, "DUMMY_PASSWORD_123!", attributes, [], (err, result) => {
      if (err) {
        console.error("❌ Error signing up user:", err);
        reject(err);
      } else {
        console.log("✅ User signed up successfully:", result);
        resolve();
      }
    });
  });
};



if fail at signUpUser 
❌ Error signing up user: [NotAuthorizedException: Client <Client_ID> is configured with secret but SECRET_HASH was not received]

So my questions are :

1- Do I have to create a new App Client with no Client Secret enabled In order to bypass the above error?

2- Should I use Identity Pool Instead of Cognito User pool to accomplish the Social Providers Authentication ?

3- Should this be done using the mentioned libraries or Amplify is needed to accomplish the Social Providers Authentication ?