A clogged HVAC drain tube will allow water to drip onto the front floor, but the water sometimes migrates to the rear. It all depends on the shape of the floor pan.
Once you find and stop the leak the padding under the carpet will have to be removed to dry. It will not dry if it stays under the carpet, and there isn’t a shop vac on the planet that can remove the water from the padding.
But first you have to find the leak.