Arihant project started as SSN design but then Indian's wanted second strike capability so they added missiles compartment what took time. If they had gone with SSN like originally planned i'd wager Indian Navy would already have few attack submarines on their fleet by now.
True, but the fact remains that India did change the Arihant from an SSBN to a SSN programme.
So they won't have any SSNs for a long time yet.
Plus I would disagree against your categorisation that China has a lot more enemies with submarine fleets than United States.
Most people and decision makers don't want or see China as an enemy. See the Pewglobal surveys or the Singapore ISEAS think tank surveys.
In Japan, 53% of people in 2015 still think China's growing economy is a good thing.
In the US, there are almost equal numbers of people to think China will never replace the US as a superpower versus the same number who believe China will replace the US.
A majority of ASEAN decision makers already rate China as much more influential.
A majority of the European public also believe China will surpass the US.
So you can see the world is really split when its comes to China, because China is simultaneously a huge opportunity but it is also seen as a fearsome and powerful competitor.