Which means that it doesn't always have negative temperature.No
You have missed the point.
It's sad, but no surprise.
You just don't seem to have what it takes to understand this.
You should probably stop wasting time trying.
The process called "laser cooling" but that is a misnomer.
You don't need a laser to do it.
Using a laser is by far the most sensible way but, in principle you could use a different light source.
So laser cooling has nothing to do with the negative temperature in a laser.