The Hopfield neural network stores memories using all-to-all-coupled spins and recalls those memories through equilibrium dynamics. Storing too many hampers recall because frustration causes an exponential number of spurious patterns to arise as the network becomes a spin glass. Despite this, memory recall can be restored, and even enhanced, under quantum-optical nonequilibrium dynamics because spurious patterns can now serve as reliable memories. We experimentally observe associative memory with high storage capacity in a driven-dissipative spin glass made of atoms and photons. The capacity surpasses that of the Hopfield model under Hebbian learning by up to seven-fold in a sixteen-spin network. Atomic motion boosts capacity by dynamically modifying connectivity akin to short-term synaptic plasticity in neural networks, realizing a precursor to learning in a quantum-optical system.