Remember that the number of missiles that an SSN can carry is very limited. And then a Chinese SSN would have to return to a port to reload, which will take days or even weeks.
I think the likelihood of solely SSN versus SSN encounters is much lower.
Prior to Patchwork's departure, he mentioned that the PLAN was working on a submarine-launched 3000km hypersonic missile. At this sort of distance, the chance of a SSN versus SSN encounter in the middle of the ocean is really low, given that the upcoming Type-096 should have a noise level comparable to background ocean noise, just like the Virginia SSN. Remember that we had the French and British SSBNs actually colliding, and both sides not realising they actually hit another submarine.
Then if we're talking about Chinese SSNs attacking US naval ships with torpedoes, I would expect some sort of opposing airborne ASW to be present.
Also, talking about prompt global anti-ship strike is a step too far at this point, because you're looking at another level of improvement in terms of terminal targeting at Mach 20? speeds.
A fixed target, such the ship in port should be feasible.
I generally use the US military as a reference for minimum size.
Personally I think the Chinese Navy will be somewhere between 1.3x to 2x larger than the US Navy, roughly speaking. This largely depends on how bad US-China relations become.
I'd go with 6 SSNs annually as an upper estimate, which is roughly 2x the US rate. Eventually you end up with a fleet size of 200-odd SSNs, which is definitely enough.
Can China militarily conquer the Philippines or Japan?
The realistic answer is no, and therefore the 1IC cannot be China's Eastern Great Wall.
But in the future, it is possible that Japan and the Philippines flips from the US to China.
Earlier this year in a podcast, I recall the Economist China correspondent musing that he could see Japan switching allegiance from the US to China. But for this to happen, I think China has to have a blue-water Navy that can wrest control of the Pacific from the US Navy. That would mean a Chinese Navy with a larger carrier fleet.