If you've already registered a subcustomer with a base configuration, you can call it to list all of the domains (subPropertyID) associated with it.

This is accomplished by running the "List all subcustomer domains" operation via the ACE API. You'll need the following values to run this operation:

• network: You need to decide which network version of the base configuration you want: production (live) or staging (testing).
• propertyId: This is the unique ID value associated with the base configuration that houses the target subcustomer. Contact your Account Representative for this value.
• sub-customerId: The ID associated with the subcustomer you want to target.

See the ACE API docs

Call formatting and specifics are covered in the API documentation:

https://developer.akamai.com/api/media_delivery/cloud_embed/v2.html#getsubproperties2