I have AWS Cognito Identity Pool that is configured with Cognito User Pool as an authentication provider.
Assume I have identity ID of an identity in Cognito Identit
AWS cognito-idp list-users has a filter option that allows you to filter based on attribute. 'sub' is the attribute that matches the identity id you are describing.
e.g. at the command line:
aws cognito-idp list-users --user-pool-id us-east-1_abcdFghjI --filter "sub=\":XXaXcXXa-XXXX-XXXX-XXX-XXXXXXXXXXXX\""
This also requires the user-pool-id, which I suspect you have. Additionally, I have no idea how this is implemented or how it performances when filtering a large number of users, but I take custom attributes not being usable in filters as a hint that there is some form of indexing behind the curtain.