This pioneering research highlights a significant stride in quantum computation, introducing a novel task for measuring Out-of-Time-Order Correlators (OTOCs). Executed on the Sycamore chip, the 'Quantum Echoes' algorithm demonstrates a verifiable quantum advantage, achieving an astounding 13,000x speedup over classical supercomputers for specific computational challenges. This groundbreaking original work paves the way for advanced applications, including Hamiltonian learning and precise characterization of molecular structures via quantum simulation and NMR spectroscopy, thereby advancing the probing of microscopic physical systems.