Precise time synchronization at the single-photon level is a key requirement for quantum communication systems, including quantum key distribution (QKD) and entanglement-based networks. We demonstrate a single-shot time synchronization method based on a non-periodic weak coherent pulse pattern combined with a pilot sequence, transmitted only once on a single optical wavelength. Despite the probabilistic nature of photon detection and the presence of dark counts, the arrival time of the pulse pattern can be reliably identified. Using superconducting nanowire single-photon detectors and time-tagged detection, experiments demonstrate a synchronization precision of 24 ps (FWHM). The proposed method operates independently of the quantum encoding scheme and requires neither repeated transmissions nor wavelength-division multiplexing, making it broadly applicable to quantum communication architectures.