The inner solar system's biggest and most recent known collision was the Moon-forming giant impact between a large protoplanet and proto-Earth. Not only did it create a disk near Earth that formed the Moon, it also ejected several percent of an Earth mass out of the Earth-Moon system. Here, we argue that numerous kilometer-sized ejecta fragments from that event struck main-belt asteroids at velocities exceeding 10 kilometers per second, enough to heat and degas target rock. Such impacts produce similar to 1000 times more highly heated material by volume than do typical main belt collisions at similar to 5 kilometers per second. By modeling their temporal evolution, and fitting the results to ancient impact heating signatures in stony meteorites, we infer that the Moon formed similar to 4.47 billion years ago, which is in agreement with previous estimates.