The full potential of pinching-antenna systems (PAS) can be unblocked if pinching antennas can be accurately activated at positions tailored for the serving users', which means that acquiring accurate channel state information (CSI) at arbitrary positions along the waveguide is essential for the precise placement of antennas. In this work, we propose an innovative channel estimation scheme for millimeter-wave (mmWave) PAS. The proposed approach requires activating only a small number of pinching antennas, thereby limiting antenna switching and pilot overhead. Specifically, a base station (BS) equipped with a waveguide selectively activates subarrays located near and far from the feed point, each comprising a small number of pinching antennas. This configuration effectively emulates a large-aperture array, enabling high-accuracy estimation of multipath propagation parameters, including angles, delays, and path gains. Simulation results demonstrate that the proposed method achieves accurate CSI estimation and data rates while effectively reducing hardware switching and pilot overhead.