Correction: I'm far from an ASW expert. My rating and initial training was in electronics used in ASW, but never worked in ASW. Of course that was never a reason not to give friends in ASW a hard time.
No sub is truly invisible in the same way that the F-117 Nighthawk is "invisible" to radar. They are just extremely hard to find hiding in all the other noise in the ocean and acoustic stratification. Radar waves through air are far more predictable than sound through ocean water. Imagine trying to listen for a Tesla on street next to a major freeway. ASW depends a great deal on computers, lots of active and passive sonar transducers, big explosions, and luck.
German fuel cell subs are relatively quiet compared to nuclear boats, largely because they don't depend on high speed steam turbines or require as many pumps. Great for spying but limited for keeping up with a carrier task force. The problem with sinking a carrier is it will result in retaliation that no attacker could win. Basically a variation on mutually assured destruction.
