What happens most of the time with the big companies (Boeing, Cessna, Bombardier...) is that it is cheaper to have an in-house DER (Designated Engineering Representative) for the part of the aircraft that they are certifying. DERs themselves

You have Mechanical DERs, Electrical DERs, Software DERs, and others.

A good example for the HN crowd, the Software DER. Per regulations, the software standard is the DO-178B. The DER isn't actually spinning up the dev environment, or building the piece of software used; just checking to make sure the process was followed. (the dev environment was documented, what dependancies...) These people are a step up from code reviewers and just check paperwork more than software.

The FAA itself isn't concerned with safety; it is just there to make sure there is a papertrail to follow in the event of a safety issue.