This could probably be achieved very simply by a device with a microphone and a script that just checks the noise level. Either checking for consistently high noise levels, or if you want to get fancy, maybe do some heuristic stuff to pick out crying specifically.
Might be a cool project to do with a cheap microphone and an SBC.
This is how a lot of baby monitors do it. Mine goes off if someone with a loud muffler drives by too which is convenient because my son will frequently be awakened by that so I get a little extra time.
Might be a cool project to do with a cheap microphone and an SBC.