How early can one check in for an international flight? We have to check ou of hotel (with late check out) at 1:00pm and flight is at 10:30pm.

Through my experience, airline counter open around 2 hours before frying. But already my peoples are lined up early than that . You can get the boarding pass at Kiosk (self check in desk), kiosk is faster than counter.

Each airline is different and depends on if they have other flights that might have the counters open already.

Different airline has different policy but they won't check in till 8 pm on your case.