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Quantum advantage, benchmarking the computational power of quantum machines outperforming all classical computers in a specific task, represents a crucial milestone in developing quantum computers and has been driving different physical implementations since the concept was proposed. Boson sampling machine, an analog quantum computer that only requires multiphoton interference and single-photon detection, is considered to be a promising candidate to reach this goal. However, the probabilistic nature of photon sources and inevitable loss in evolution network make the execution time exponentially increasing with the problem size. Here, we propose and experimentally demonstrate a timestamp boson sampling that can reduce the execution time by 2 orders of magnitude for any problem size. We theoretically show that the registration time of sampling events can be retrieved to reconstruct the probability distribution at an extremely low-flux rate. By developing a time-of-flight storage technique with a precision up to picosecond level, we are able to detect and record the complete time information of 30 individual modes out of a large-scale 3D photonic chip. We successfully validate boson sampling with only one registered event. We show that it is promptly applicable to fill the remained gap of realizing quantum advantage by timestamp boson sampling. The approach associated with newly exploited resource from time information can boost all the count-rate-limited experiments, suggesting an emerging field of timestamp quantum optics.