What is Galilean invariance? You are below deck in a ship moving uniformly on a smooth sea. No experiment can tell you if the ship is docked or if it has motion relative to the see. Assume that the ship is docked. In that case you say that the ship is at rest. And you attribute to the ship some properties because it is at rest. But is the ship at rest absolutely? Not at all. The ship is moving with the earth. So do you deny that the earth is moving? I assume not. If so how can you claim that the ship is at rest?

Motion is absolute means that all is in motion. This is an axiom. When you say motion is not absolute, can you give an example of an object which is at rest, which does not move with the earth and does not move with the galaxy? There is no such object.