We put the crib close to our bed, much easier for mom. Dad got ear plugs.
Nature does so much to bring mothers closer to their young, yet fathers do not possess this "talent." In fact, we seem eager to block out some of that natural closeness we feel towards our children. We use ear plugs now, but I am sure we used animal fur and cotton to achieve the same effect centuries earlier.
That has nothing to do with being a mother and everything to do with spending a lot of time with that child. I'll bet that anybody who spends enough time with a child will be able to do that, regardless of that persons gender or genetic relation to the child.
To address your specific point, though, which was echoed by others in this thread, there is a lot of truth to the human ability to hone their auditory memory, especially when it comes to sounds that fall within the human auditory frequency range. Many of us have experienced this phenomenon not only with their own and others' children, but also with their house pets (especially cats and parrots), and even machines (i.e., your car, your air conditioner, your server, etc.)
Nonetheless, as I have shown, there is a particular biological difference exhibited between first-time mothers and first-time fathers. Nothing about this statement invalidates or calls into question your own statement and I agree with it wholeheartedly.
Towards the end I could tell, from the sounds of his crying, whether he was hungry, tired, or hurt too. (Towards the end in the sense that he was able to answer questions, or use words to explain a little what was going on. Raising him bilingually, and it took a while for him to start speaking.)
First off, I thought it was a lot more conventionally understood that mothers' bodies undergo permanent hormone-driven changes during pregnancy - and that these changes yield some more-or-less common outcomes across cultures and locales. [0] One of those outcomes is the following:
> The researchers found that the mothers had surprisingly consistent responses to their crying babies, “and in a very short amount of time from the start of the cry, five seconds, they preferred to pick up and hold or to talk to their infant,” Bornstein said.
I also thought it was much more conventionally understood that fathers do not exhibit the same changes as mothers do. [1] Nevertheless, I want to make it clear that I do not have children. My understanding of this phenomenon stems from my background in psychoacoustics, not child-rearing.
Second, though, and perhaps more importantly, I am pretty disappointed in this community for laboring to interpret my points as misogynistic, out of touch with modern norms, or whatever, when a simple google search would have easily brought my points into context. Perhaps I failed to follow the conventions of citing resources to learn more about these things, but as I already indicated I didn't do this because I thought the majority of those commenting would have already been aware of this research. I apologize for not including it and I will try to do better in the future.
[0] https://www.cnn.com/2017/10/23/health/moms-babies-crying-res...
[1] https://www.nih.gov/news-events/news-releases/womens-mens-br...
All humans have the capability to intricately form an aural bond with their own (and other) children if they have enough meaningful interactions with that child. But there is nonetheless a specific change brought about in women during their first pregnancy that gives them an advantage on this front, especially with their own children.