The short answer is that unfortunately it's practically almost impossible to do this any other way, short of massively increasing funding for the FAA (which is presumably politically not going to be done.)
The long answer is, anyone with expertise ends up going to work at an aerospace company where they are properly compensated. You end up with the engineers at Boeing et al, and the regulatory folk at FAA etc. (This isn't unique to just aviation btw but most industries where you need a high level of technical expertise.) And if you think it should be easily doable... here's a thought experiment. Say 20 people in boeing know about MCAS (pre crashes and their publicity). If even only 2 FAA employees need to be technically sound in their knowledge of such a niche system, that's about 10% of how many boeing employees know about it.
Now if you extrapolate that to all systems and all employees across multiple companies... you see why it's an issue for one agencies to have such deep knowledge about everything. (And this isn't even considering what happens when people quit etc.)
Because of this, the most obvious answer to "how does the FAA, without much engineers, decide what's safe or not", is to ask the experts and just have them certify stuff, well, not under oath, but as close to that as possible.