contrast to previous works with multiple junctions and an additional charge island for the QCR, we galvanically connect the NIS junction to an inductively shunted electrode of a superconducting microwave resonator making the device immune to low-frequency charge noise. At low characteristic impedance of the resonator and parameters relevant to a recent experiment, we observe that a semiclassical impedance model of the NIS junction reproduces the bias voltage dependence of the QCR-induced damping rate and frequency shift. For high characteristic impedances, we derive a Born–Markov master equation and use it to observe significant non-linearities in the QCR-induced dissipation and frequency shift. We further demonstrate that in this regime, the QCR can be used to initialize the linear resonator into a non-thermal state even in the absence of any microwave drive.