In the context of hybrid quantum systems, there is a demand for superconducting tunable devices able to operate in the single-photon regime. In this work, we developed a 3D microwave reentrant cavity with such characteristics ready to provide a very fine-tuning of a high-Q resonant mode over a large dynamic range. This system has an electronic tuning mechanism based on a mechanically amplified piezoelectric actuator, which can set the cavity resonance with a large dynamic range of order 1 GHz at 10 mK. At elevated microwave power, nonlinear thermal effects were observed to destroy the superconductivity of the cavity due to the large electric fields generated in the small gap of the reentrant cavity.