[en] Here, we present the first laboratory generation of high-Mach-number magnetized collisionless shocks created through the interaction of an expanding laser-driven plasma with a magnetized ambient plasma. Time-resolved, two-dimensional imaging of plasma density and magnetic fields shows the formation and evolution of a supercritical shock propagating at magnetosonic Mach number M_ms ≈ 12. Particle-in-cell simulations constrained by experimental data further detail the shock formation and separate dynamics of the multi-ion-species ambient plasma. The results show that the shocks form on time scales as fast as one gyroperiod, aided by the efficient coupling of energy, and the generation of a magnetic barrier between the piston and ambient ions. The development of this experimental platform complements present remote sensing and spacecraft observations, and opens the way for controlled laboratory investigations of high-Mach number collisionless shocks, including the mechanisms and efficiency of particle acceleration.