If first submarine is launched in 2022 (that's a wild guess, of course) then taking into consideration the learning curve modeled after US Virginia subs' building experience, the next submarine from the same spot might take some 3 years. BUT, since there may be room for partial build of another submarine in the same spot, it might be even a bit less. Certainly over time, as the learning curve is overcome, it will indeed become quicker.
2022 first SSN
2023 second SSN
2024 third SSN
then the subs built behind those in the same assembly line get moved forward and finish up.
2024/2025 fourth SSN
2025/26 fifth SSN
26/27 sixth SSN
then 2.5 more years for another batch which started assembling from 2024/2025 onward. So those get launched:
2027 seventh SSN
2028 eight SSN
2029 ninth SSN
By then the assembling process might get even better so I'll use just 2 years from start of assembly to launch
2029 10th SSN
2030 11th SSN
2031 12th SSN
Of course, if could be even quicker. Virginia, with its premade and prefurbished large modules is at mere one year from start of assembly to launch. There's no telling what exact process will be used nor what the assembly halls will be used for.
For example, china might go down the same route as Virgina, with prefurnished modules made in the northern building and then there'd be room in the assembly halls for one a half submarine at a time.
Or the nortern hall might be making empy hull modules which then get moved to the assembly hall and which are then furnished there, propulsion is added there etc etc. That might take up pretty much the whole length of one assembly line. Or it might not. who knows?
And of course, with the added hall with two more lines, it seems there will be enough room to add SSBNs produced on top of these SSN numbers. Possibly starting 3 years after the first SSN, so 096 class being launched around 2025? And due to complexity slightly more time might be needed per sub? Resulting not in 12 subs in 10 years but say 9 or so, if there were 3 lines. Since there are two lines, that's really 6 SSBNs from 2025 to 2034. This assumes the original 094 assembly hall is not used for further subs, though.
Disclaimer: Of course these are just one person's musings. Different opinions and schedules were offered by different people before. And I'm sure yet different ones will be offered by other people in the future.
The way I see it, this yard is trying to efficiently divide the labour of the different stages of construction as much as possible.
Having a dedicated massive pressure hull facility and a dedicated even larger assembly hall and even a dedicated paint shop all attests to that.
One of the key questions you touch on, is how long each SSN "slot" in the assembly hall actually needs to be used for the actually assembly part of the submarine, because you shouldn't be spending three whole years in an entire slot from the first fabrication of the pressure hull to launch (fabrication being done elsewhere).
Like... the fact that they have a dedicated paint hall sized for SSNs rather than just doing the paintwork in the assembly hall like basically everyone else does, suggests to me they recognize that time in the floor space of the assembly hall is valuable and you'd want to maximize turnover and minimize time spent in each assembly slot.
The configuration of this entire facility is overwhelmingly suggestive of a desire for fast turnover. The question is how quickly the PLAN will take advantage of it, how fast the facility can ramp up, and how much of the floor space will ultimately be exploited.
The fact they're building an entire new assembly hall that looks like it's sized dedicated for SSNs, well before the first submarine from the new facility has even been launched (or even started assembly as far as we know), only credibly points in one direction, which of course is quite consistent with the PLAN's own likely obvious recognition of the need to rapidly procure a large and capable SSN fleet once the technology and design for a competitive type is ready...
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Also, I'm not sure why you're talking about SSN production in batches of "three". If that idea is based off SSNs being produced from the existing new eastern assembly hall being fully utilized for SSN production (no SSBNs), there are actually
six 7.34m gauge tracks for SSNs in that existing eastern assembly hall.
The new southern hall being built has an additional
four 7.34m gauge tracks for SSNs.
If we're talking SSN line equivalents, it's
six and
four lines respectively, not three and two.
This of course ignores the total length of the tracks in each assembly hall, which is well over double the length of a contemporary SSN.
... If we are talking hypothetical SSN "slots," then it's
twelve and
eight, aka
20 SSN slots.
Of course, chances are, for part of the time to assemble an SSN the total length you need will be longer than a single SSN slot, so obviously you're not going to be simultaneously assembling a total 20 SSNs simultaneously in both the eastern and southern assembly hall, not least because part of the eastern hall will always be allocated to building SSBNs or large payload submarines most likely.
edit: I made this quick and dirty comparison of the eastern assembly hall scaled with Virginia SSNs and Ohio SSBNs at the same visual altitude a few years ago on CDF specifically to demonstrate this, I'm not sure if you've seen it...