I once was taking an early connecting flight from Florida to NYC to HKG...the connecting time is definitely not enough so I booked the ~2 pm flight JFK-HKG flight and hoped that I could make it to get on the ~10 am flight. but finally I just missed it by 10 mins or so.

by that time the CX check-in counters were closed (the J/F side) (and BA's also not open I think?) anyway, I sat there for some 15-20 mins checking emails and then decided to walk around instead of just waiting. then I found actually the CX counters are still open on the Y side (it's in another row, so I didn't check, I assumed J/F closed = Y closed as well, but it's not in fact). so...it looks to me that if you arrive too early, you might have luck checking in at the Y counters even if the J/F counters are closed. the Y counters might be open nonstop in the day ? (just 1-2 of them instead of full set of Y counters of course)