Set Up Google as a social identity provider in an Amazon …

Note: In the app client settings, the mapped user pool attributes must be writable. For more information, see Specifying identity provider attribute mappings for your user pool.. In the Amazon Cognito console, choose Manage user pools, and then choose your user pool.; In the left navigation pane, under App integration, choose App client settings.; On the app client page, do the following:

https://aws.amazon.com/premiumsupport/knowledge-center/cognito-google-social-identity-provider/