Amazon Cognito is the correct AWS service for this requirement because:

• Amazon Cognito provides user identity and data synchronization that enables you to securely manage and synchronize app data for your users across their mobile devices
• It supports federated identity through social identity providers (IdPs) like Facebook, Google, Amazon, and others
• It allows users to sign in with their existing social media accounts rather than creating new credentials
• The other options are not designed for this purpose:
  • AWS Lambda is a serverless compute service for running code
  • AWS Secrets Manager is for managing secrets and credentials
  • Amazon CloudFront is a content delivery network (CDN) service