It may not be needed at the time the engine is running because the engine may not be hot enough... hard to tell without the model and engine type

Is the fan mechanical or electric? Either way on newer cars the fan is thermostacally controlled. If its an electric fan it should come on as soon as you turn on your air conditioning. That is one way to check it.

Because engines are designed to run between 190 to 210* in modern day cars.
Too cold is very inefficient and bad for emissions. Too hot is bad for the motor itself.
That's why we rely on temperature sensors to "trigger" the fans on when needed for optimum performance.
A/C on the other hand is heat no matter which way you look at it, so fans are needed all the time with A/C on.
Sometimes slow, then sometimes fast. That all depends on the pressure building up inside the lines.
Pressure sensors take care of that job.
Cooling systems are one of the most overlooked areas under the hood but plays a VERY important role!
Clear things up?

https://www.askmehelpdesk.com/cars-trucks/when-asking-about-your-vehicle-303903.html