I've attended a presentation at an EAA chapter, by an FAA inspector, regarding his work on an EXP airworthiness inspection.
His inspection consists of looking the plane over, looking the build logs over, checking the paperwork details, and doing a hands-on check that the flight controls are functioning correctly. He is looking for key screwups that can affect newly built experimentals.
There is no engine run-up to verify any aspect of engine operation.
It is not a comprehensive inspection of the aircraft by any means. He does not have time to do an inspection as detailed as an annual inspection, for example, which would take many, many hours.
I personally would hire an A&P or AI to inspect the aircraft.