This work presents the development and experimental characterization of a compact ultraviolet (UV) telescope based on silicon photomultipliers (SiPMs) designed for the detection of faint atmospheric optical tracks. Such transient optical phenomena include meteors, transient luminous events (TLEs), space debris reentries, and other faint atmospheric emissions. Nuclearite-induced atmospheric emission is considered as a benchmark case for evaluating the expected signal levels of rare luminous track events. We detail the fabrication, assembly, and testing of the SiPM sensor array, comprising parallel Geiger-mode avalanche diodes with high fill factor and photon detection efficiency, alongside custom readout electronics using self-triggering ASICs, precision optical components, and a stable mechanical mount. This photon-counting telescope provides a compact and mechanically robust alternative to conventional PMT-based systems, with demonstrated capability for detecting low-light atmospheric tracks under controlled laboratory conditions.