One of the most basic tasks to characterize analog quantum simulators is to estimate the many-body fidelity between an ideal target state and the state obtained from experiments. In this talk, I will present a simple and efficient benchmarking method that requires minimal experimental control. It only requires time-evolving a quantum system under its natural ergodic dynamics, followed by measurements in a fixed local basis. At its core, our method is made possible by using a newly-discovered phenomenon that occurs in strongly interacting quantum many-body systems, namely the emergence of universal random statistics. I claim the phenomenon occurs universally in a wide class of ergodic quantum systems at infinite temperature by presenting a number of evidence based on solvable models and numerical simulations. I will discuss our benchmarking protocol based on the emergent randomness, and demonstrate it both numerically for model systems and experimentally using a Rydberg quantum simulator.