If they knew they were taking off at 0545 than they also knew they would need to contact tower. The airport goes controlled at that time. In fact stating it was 0545 makes the situation a bit worse. A takeoff from a controlled field without clearance.
I suspect with a scheduled push time of 0540 crews often tried to get off the gate a bit early so they could depart prior to 0545 and avoid having to talk to tower and a possible delay. I don't know why they did not make the required CTAF radio calls or even monitor the frequency. It's possible maybe they had the wrong frequency dialed in as I can't see a airline crew skipping those calls.