Yes, it's possible to programmatically create and associate a Box App User with a Salesforce Experience Cloud user using Apex and the Box SDK. Since the standard integration doesn't handle this, you need to write custom Apex code to first authenticate using a JWT connection, then call the `BoxUserAPI.createAppUser()` method. After the Box App User is created, you must store its unique ID in a custom field on the Salesforce user's record. This association allows subsequent API calls to be made on behalf of the Experience Cloud user, enabling a seamless and secure headless integration.