Many chats later and I had one tech tell me that it "would be very illegal for Cox to control the firmware on the MODEM".
This tech didn't know the answer to the question so they started making stuff up rather than just escalate the issue to someone who could give you a correct answer. They will probably continue to give bad advice to other customers until they are terminated.
The other answers in this thread are correct. Your modem will automatically receive a firmware update when it has been approved by Cox and deployed on the Cox network. You don't need to do anything to receive this firmware update. In almost all cases, whatever issue you're having is not related to the firmware version so if you have issues you should explore other possibilities beyond the firmware version.