The unclassified evidence is that it was, and remains, very difficult to track down the location of a properly operating and operated ballistic missile submarine. Some of the reasons for that have already been mentioned. Some exotic technology has been looked at (and will doubtless continue to be) for ways to detect submerged submarines of any type.
The actual and most practical tactic most often used seems to be to have an attack sub lie quietly in the expected path of newly deployed, outbound ballistic missile subs, then to follow in their wake (“baffles”) where the pursuer can remain hard to detect from the missile sub. For this reason, on occasion friendly attack subs follow the ballistic missile subs out to sea, at a discrete distance of course, in an attempt to intercept any hostile attack subs that may try to do this.
There are a great many such “games” of skill and danger that go on in submarine missions and we, the public, will seldom, if ever, know of any of it.
BTW, I was not a submariner myself, but was for some years assigned to US Navy antisubmarine aircraft squadrons who tried to make life miserable as possible for Soviet submariners, even in peacetime. If we could locate one (which was fairly easy, they were very noisy back then) we’d harass them unmercifully with small noise bombs until we forced them to surface for the rest of their voyage to wherever it was they were deploying to - usually Cam Ranh Bay in Viet Nam or other ports operated by Soviet clients.