I think you are working to a false premise.
It is not actually the sensitivity of the microphone that is they key to this - you can take any half decent mic & keep turning it up. Sure, there will be some noise floor, but this is almost irrelevant.
What is different is perception.
The human ear is controlled by the human brain. Aside from the fact that our binaural hearing can also tell direction, we have selective attention.
This enables you to hear one person talking to you in a crowded bar, or to pick out the sound of a baby crying from three rooms away, against a backdrop of other domestic noises & traffic passing outside.
If you recorded those ambiences through a microphone, you then lose the selective attention. A mic will not differentiate between the sounds & will present them all as they actually happened. Because you no longer have your binaural senses you will also be far less capable of actually selectively picking out the one part of that overall ambience that you wish to hear in more detail.
You can get binaural mic setups [they generally look like human heads with mics in the ears] that attempt to emulate how the human ear recognises spatial differentiation, but no matter how much work they put into this field of research, I have yet to hear any convincing result - because you have to play it back on headphones, which immediately loses most of the directional aspect.