How long from ground breaking to operation... This is a mixed question it can be as little as a few days to a year or more.. here is why.
For the Few Days" they haul a "Dog house" (As the shack at the base is called) in on a truck and set it down.. Hook up power and such, Attach the antennas to the tower hook them up do their testing and go live.. Total can be done in a week or less if you have a big enough crew on the tower.
However some companies prefer to "Stick build" (it is a block house though so its Masons, not carpenters) the dog house.. Then some companies may not have all the needed permits and licenses yet when they start construction.. Some are still paying bribes (long story) and all this takes time.
So, it varies.