The geopolitical change would be dramatical once Taiwan is occupied. PLAN can begin to build bases as well as training to hunt US SSBNs even without enough SSNs, at least I can hardly find any reasons why they wouldn’t do that.
Hypothetically taking Taiwan does not mean that the PLAN would suddenly be able to credibly start hunting USN SSBNs that operate around the globe.
I think you are severely underestimating the challenge of operating at global distances (in both the pacific and the atlantic), not only in terms of the number of SSNs needed, but also in terms of global naval basing and air supports that would be needed, not to mention the extent of US and US allied global basing (not only in the western pacific, but in the overall pacific and the atlantic) that they would have at their disposal to in turn hunt Chinese SSNs.
The extent of that basing availability is a matter of very long term grand strategy.
If the PLAN has 100+ SSNs and if they have a dozen large air-naval bases scattered around latin america, africa (both the pacific and atlantic sides),
and if they've significantly rolled back the US presence in the western pacific,
and if they've managed to retake Taiwan and to somewhat finlandize Japan and South Korea -- then realistically hunting USN SSBNs might be able to be done in the way you describe.
Because what you're suggesting is the way in which the US hunted USSR SSBNs during the cold war -- and that was only possible due to the extent of US geopolitical containment (including requisite extensive basing and allies) of the USSR on both the atlantic and pacific sides. China would somehow be able to do at least a fraction of that to the US on its own peripheries.
My personal advice for you on this matter, is to not fantasize about it.
So many other things would have to happen first, that it is not worth pondering at the moment.
This will be my final post on the matter in this thread.