There's a Plaza Premium Arrivals Lounge that's open 24 hours. It's at Level 3, Arrivals Level, Terminal 2 (non-restricted area) so you'll have to take the walkway from Terminal 1.
https://www.prioritypass.com/en/loun...premium-lounge
CX does have an arrival lounge for First and Business passengers that opens at 05:00. It can also be used by some Marco Polo Club members and
oneworld frequent flyers.
Unfortunately HKG is not like SIN, which has loads of things to do. There are some arts and cultural stuff to wander through, but IMAX, the Aviation Discovery Centre, etc. open later.