Is it possible to prevent UsernameExistsException from happening for AWS Cognito?

Question

I feel that it is unsafe for UsernameExistsException to happen when a user tries to sign up with an email address that is already created because a hacker can just use random email addresses to try signing up to check if an account has been created for such emails.

Ideally, AWS Cognito will not throw an error when an already-used email address is used for signing up and instead return a successful response, sending an email to the address that someone attempted to sign up.

Is this possible to do in AWS Cognito? I've checked these pages so far but had no luck.

https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-user-pool-managing-errors.html

https://docs.aws.amazon.com/cognito-user-identity-pools/latest/APIReference/API_CreateUserPool.html