Built on Flax (ascl:2504.026), DeepSSM emulates gravitational wave (GW) spectra produced by sound waves during cosmological first-order phase transitions in the radiation-dominated era. It uses neural networks trained on an enhanced version of the Sound Shell Model (SSM). The code provides instantaneous predictions of GW spectra given the phase transition parameters, while achieving agreement with the enhanced SSM model. DeepSSM is particularly suitable for direct Bayesian inference on phase transition parameters without relying on empirical templates, such as broken power-law models.