From the dynamics of a broad class of classical mean-field glass models, one may obtain a quantum model with finite zero-temperature entropy, a quantum transition at zero temperature, and a time-reparametrization (quasi)invariance in the dynamical equations for correlations. The low-eigenvalue spectrum of the resulting quantum model is directly related to the structure and exploration of metastable states in the landscape of the original classical glass model. This mapping reveals deep connections between classical glasses and the properties of SYK-like models.