Aluminum foil under anti-static discharge mat
If your mat is an dielectric, it won't allow charge to flow from its top side to its bottom side and through the metal to ground. So, if your mat is actually a proper dielectric, this won't help.
However, your testing method is incorrect: the standards for such mats require a resistance of several megaohms (over about 30 cm or so, can't fully remember) when pressing large-diameter (thing: coffee mug crossection) metal electrodes with some serious force (&gt;20 N, IIRC) to the mat to test. Compare the cross-section of your multimeter's probe to that: no wonder it doesn't see any conductance!
You could probably emulate such tests with e.g. a small 5cm diameter puddle of soapy saltwater for each multimeter probe (or of course, ECG gel), and come barely into the region of resistances your multimeter can measure. I haven't tried that, though!