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The Probabilistic Value-Added Bright Galaxy Survey (PROVABGS) catalog will provide the posterior distributions of physical properties of >10 million DESI Bright Galaxy Survey galaxies. Each posterior distribution will be inferred from joint Bayesian modeling of observed photometry and spectroscopy using Markov Chain Monte Carlo sampling and the Hahn et al. stellar population synthesis (SPS) model. To make this computationally feasible, PROVABGS will use a neural emulator for the SPS model to accelerate the posterior inference. In this work, we present how we construct the emulator using the Alsing et al. approach and verify that it can be used to accurately infer galaxy properties. We confirm that the emulator is in excellent agreement with the original SPS model with ≪1% error and is 100× faster. In addition, we demonstrate that the posteriors of galaxy properties derived using the emulator are also in excellent agreement with those inferred using the original model. The neural emulator presented in this work is essential in bypassing the computational challenge posed in constructing the PROVABGS catalog. Furthermore, it demonstrates the advantages of emulation for scaling sophisticated analyses to millions of galaxies.