Considering that each nuclear sub has 80-100 warheads that are enough to destroy an entire continent, and considering it takes about an hour to fire them while underwater, do you suggest to attack the subs before they fire or after? How do you suggest to locate them?
Do you think that the US doesn't actively track the location of Russian missile subs? There's a limited number of sub pens and they're visible on satellite. And tracking missile subs is a big part of the attack sub's role.
I'm not saying it's perfect, but it's not nearly as impossible or hopeless as you seem to think.