Is there any way to algorithmically determine audio quality from a .wav or .mp3 file?

Basically I have users with diverse recording setups (i.e. they are from all over the world and I have no control over them) recording audio to mp3/wav files. At which point the software should determine whether their setup is okay or not (tragically, for some reason they are not capable of making this determination just by listening to their own recordings, and so occasionally we get recordings that are basically impossible to understand due to low volume or high noise).

I was doing a volume check to make sure the microphone level was okay; unfortunately this misses cases where the volume is high but the clarity is low. I'm wondering if there is some kind of standard scan I can do (ideally in Python) that detects when there is a lot of background noise.

I realize one possible solution is to ask them to record total silence and then compare to the spoken recording and consider the audio "bad" if the volume of the "silent" recording is too close to the volume of the spoken recording. But that depends on getting a good sample from the speaker both times, which may or may not be something I can depend on.

So I'm wondering if instead there's just a way to scan through an audio file (these would be ~10 seconds long) and recognize whether the sound file is "noisy" or clear.