This study reports the fabrication of the first ceramics-thermosetting polymer composites by the cold sintering process, for high ceramic volume fractions (v/v >95%). The (1 - x) ZnO - x polydimethylsiloxane (PDMS) composites, with 0.00 <= x <= 0.05, were cold sintered at 250 degrees C, 320 MPa for 60 minutes. In situ densification studies conducted with the help of a semi-automated press revealed that the mechanisms driving the densification of the material changes with the polymer content. Relative densities of the (1 - x) ZnO - x PDMS composites (0.00 <= x <= 0.05) were above 90%. Impedance spectroscopy of the composites yields insight into the ceramic-polymer interfaces within the sintered ZnO bulk and suggests long-range conduction governed by ZnO-PDMS interface properties for x = 0.03 and x = 0.05. The study also emphasizes on the complexities and opportunities of such ceramic-dominated ceramic-polymer composites.