Even if you assume the centre of mass of the universe to stay fixed, if all particles in the universe except one blinked, then you would see the one particle that didn’t blink being kicked the opposite direction; if half the particles in the universe blinked, you would see those which blinked being kicked at half the speed, and those which didn’t being kicked at half the speed in the opposite direction, etc. So it’s not like the case when all particles blink is the only special one.
Even if you assume the centre of mass of the universe to stay fixed, if all particles in the universe except one blinked, then you would see the one particle that didn’t blink being kicked the opposite direction; if half the particles in the universe blinked, you would see those which blinked being kicked at half the speed, and those which didn’t being kicked at half the speed in the opposite direction, etc. So it’s not like the case when all particles blink is the only special one.