What proves that the FCC has issued an operator/primary license grant?

The definitive proof that you hold an active amateur radio license is its presence in the FCC's Universal Licensing System (ULS) database. Once your call sign and license grant appear online in the ULS, you are officially authorized to begin transmitting. Your Certificate of Successful Completion of Examination (CSCE) only proves you passed the test; it does not grant you immediate operating privileges for a new license. Similarly, emails from examiners or testing coordinators are just notifications, not the legal proof of a license grant.