In Ubuntu 18.04, I start Clementine Music Player, but no window is coming up. But once I start Clementine another time, it comes up.

This is not a bug, it is a setting. So this is what you want:

Tools -> Preferences -> Behaviour -> When Clementine starts -> Always show the main window

No, you are not alone, it is you, me, and a bunch of other people.