9:00 am KAL business class departure from ICN terminal 2

5:40am is cutoff time for check in (3h20m prior to flight departure).

City Airport terminal opens at 5:20am.
Departure Immigration opens at 5:30am.

Is it possible to make all these deadlines first thing in the morning or is it too likely that I will miss the deadlines if there’s just a tiny delay somewhere in the process? should I expect lines/wait times at the city terminal?

Or should I just scrap the whole idea and be safer by heading directly to ICN for check in there?