Incidentally, speaking of things popping into existence (watch closely)...
Source: https://youtu.be/49e1AfwsfaE?t=154
I suspect this is the entire reason for the moving search zone mechanic. It's pure misdirection to make sure you're looking the other way when the base does indeed pop into existence. I have to say I think it's actually quite a clever solution to a technical problem (the only issue is that they broke it a while back with the initial jump now being too far away).
Would it kill them to bring the mission objective into existence as soon as you do your initial scan in-system? I genuinely don't believe so.