@christopher.eugene.r we do not have an endpoint that doesn’t require an access_token that will allow you to check this information. At Auth0 we do not like having a publicly exposable endpoint allowing you to check user existence. This would allow a user to discover all your users’ emails. The only way you can get this information is trying to register a user that already exists.
You could, with a token, call the users-by-email endpoint to check if a user exists by email:
or user search endpoint for username: