Installing an air gap in a concrete countertop
To install faucets or air gaps in thick countertops, simply bore a wide hole (2 1/2 - 3 inches) from the bottom of the countertop halfway through or so.  In your case, they'd have to bore a wide hole at least 3/4 inches up from the bottom.  The hole just needs to be wide enough to provide room to secure the nut.

In concrete countertops, the forms are made with holes pre-cast wide at the bottom and narrow at the top.