What was your possible exposure?
The PCR test is not considered a primary diagnostic test. A 4th or 5th generation Ag/Ab test is recommended 28 days (or more) post-exposure. If not available, an antibody-only test will be conclusive at 90 days post-exposure.
Since PCR tests are very sensitive and directly looks for the viral genome. A PCR RNA, theoretically can be used to determine infection as early as 72 hours post transmission. However, as stated by CurfewX, it is not a recommended test for primary diagnostic purpose.
I am assuming that you have taken an RNA PCR and not a DNA PCR at 12 days because RNA PCR is the test that is recommended to be best taken at 10-14 days, if someone has an exposure with a known positive partner.
Since the viral replication post transmission is high and PCR RNA looks for the infected RNA with sensitivity of as low as 20-50 copies, the chances of missing an infection is substantially low.
Your risk was low, plus an undetected RNA NAT only suggests you weren't infected from your event. As suggested by CurfewX, you will have to back this result up with a standard antibody test, that's the testing protocol. Timelines for testing is already provided to you.