America west had plenty of flights out of LAS leaving really early. (I had an LAS-SLC just after midnight)

Anything out of DEL also tends to leave in the early hours of the morning.

a few weeks back my ORD-MSY flight was pushed back to 00:07am...

But those are all more late-night than morning.

As for legit 'morning' flights. UAs 6:00 ORD-DEN is always packed on Mondays. I've also done a 5:55 Delta. (That is now pushed back to 6:00)

Though the earliest I've done recently was DAY-MDW and MDW-DAY. My outbound was MDW-DAY leaving at 5:45am. However, the aircraft originates in DAY, and for the return, I took the 5:15am DAY-MDW flight. (The times have since been pushed back a little) Surprizingly the flight only had a couple of empty seats. That the earliest 'legit' morning flight I've been on.