I doubt the Navy wants to advertise the details of its underwater surveillance capabilities to America's enemies.
Plus, there are lots of noises under the ocean, many geological.
The U.S. government's hydrophone network has been known about for decades - at least in terms of its existence, if not specific details - and the Soviets/Russians most likely knew where a lot of the listening equipment was located.
That being said, these things are apparently extremely sensitive, and extremely good at discerning the acoustic signatures of various underwater mechanical failures from naturally-occurring sounds.
Even back in the 1960s, the equipment was apparently good enough that it was able record sounds from the Scorpion incident that allowed later researchers to identify various specific events, or likely events, in the course of that submarine's failure, sinking, and ultimate destuction from compressive implosion.
That was almost 60 years ago, and I'm quite sure the equipment has been updated a time or two since then, so it is entirely possible that the system, just set on its default recording procedures, was able to pick up the particular signature of the Titan's implosion.
Furthermore, the Navy apparently started reviewing the acoustic data shortly after they learned that the submersible was not responding to contacts, and detected that signature. They also apparently were able to use the acoustic data to start narrowing down the likely location of the debris field.
To me, the three question are (a) how confident were they in that identification, (b) how quickly did they convey that information to the company itself, and (c) why wasn't it disclosed to the public earlier than it was?