A MEMS acoustic transducer device has a capacitive microelectromechanical sensing structure and a biasing circuit. The biasing circuit includes a voltage-boosting circuit that supplies a boosted voltage on an output terminal, and a high-impedance insulating circuit element set between the output terminal and a terminal of the sensing structure, which defines a first high-impedance node associated with the insulating circuit element. The biasing circuit has: a pre-charge stage that generates a first pre-charge voltage on a first output thereof, as a function of, and distinct from, the boosted voltage; and a first switch element set between the first output and the first high-impedance node. The first switch element is operable for selectively connecting the first high-impedance node to the first output, during a phase of start-up of the biasing circuit, for biasing the first high-impedance node to the first pre-charge voltage.