Our military would have known immediately if a missile was fired.
They can't even find the plane, and aren't sure where it was at.
PLUS, there were reports that NK did fire a missile in some kind of 'exercises' near to where the airliner was thought to be. We know that tensions between NK and SK are very high. NK has a huge number of anti-aircraft batteries. How easy would it be for a test missile to end up latching on to a stray airliner ?
Did the NK try to contact the airliner (like others did) and getting no response, assumed it was some kind of attack ?
For all we know there could have been multiple missiles fired the day this airliner disappeared. I don't see how our military would know , and if they did, they might have been told to keep it quiet for now.