two thoughts:
A bare Piezo element soldered to the top surface of the PCB, with a narrow piece of copper tape to the element (you will either need to trim the backing plate where the tape is, or insulate between the copper tape and the backing plate) this will add maybe a couple of mm thickness.
or if this is a problem, get a hole milled (or drilled) in the PCB, sit the element in the hole, carefully run a bead of epoxy around the edge, gluing the back-plate to the PCB.
Or, maybe a better idea, make the hole slightly smaller than the Piezo element, so you can sit the element on the underside of the PCB, then solder around the edge of the back plate, and bridge between the element and a track on the front of the PCB, which again could be done using a small piece of copper tape, in order to keep the design flat.