Something the size of HSU-001 definitely does not need a dedicated submarine yard to build, and certainly not nuclear certified yard. Huludao will build non-nuclear subs long before they start building UUVs, and there's no evidence they're doing even that.
The point is that in terms of shipyards used to building military grade underwater vehicles, you've only got Huludao and Wuchang. Given that UUVs are likely the next progression in underwater technology, it is logical to use these 2 existing shipyards. Remember that they both have commercial shipbuilding businesses, which are obviously not nuclear-certified.
The USN currently has 53x SSN, 13x SSBN and 4x SSGN for total of 71, it building 1.5x Virgina a year trying to ramp up to 2 a year, has a total of 12x Columbia ordered that won't enter service until 2030s, all 4x SSGN are schedule for retirement by 2028 and almost all Los Angeles boats will be retired by 2035, which means in 10 years US will have, assuming they can ramp up Virgina and Columbia stays on schedule, ~40x Virginia SSN, ~14x Ohios and ~2x Columbia.
So even if we start at 6+6 for China today (it's almost certainly higher), and not counting the 4 new bays added at Huludao, not counting bays prior to 2016 expansion, not counting conventional subs or semi-nuclear subs, in 10 years we're looking at conservatively 72x vs 56x, and if that's not enough for dominance, then give it 15 years for China 100 vs 70.
Sure submarines alone isn't enough to ensure global dominance over USN, which is where China's massive surface fleet construction and global prompt strike systems comes in. Remember, SSN was the USN's last saving grace.
Even 100 vs 70 isn't enough for dominance. Remember that "dominance" comprises domains underwater, on the surface and in the air.
Currently, Chinese SSNs operating beyond the 2IC will be operating alone in a high-intensity conflict. So when these Chinese SSNs approach an enemy CSG, the SSN will face a situation where the other side has control of the air, and therefore the ability to use helicopters and MPAs to go after the SSN.
Therefore Chinese dominance will also require enough aircraft carriers, which will probably take another 10-15 years.