Full-physics cosmological simulations are powerful tools for studying the formation and evolution of structure in the universe but require extreme computational resources. Here, we train a convolutional neural network to use a cheaper N-body-only simulation to reconstruct the baryon hydrodynamic variables (density, temperature, and velocity) on scales relevant to the Ly alpha forest, using data from Nyx simulations. We show that our method enables rapid estimation of these fields at a resolution of similar to 20 kpc, and captures the statistics of the Ly alpha forest with much greater accuracy than existing approximations. Because our model is fully convolutional, we can train on smaller simulation boxes and deploy on much larger ones, enabling substantial computational savings. Furthermore, as our method produces an approximation for the hydrodynamic fields instead of Ly alpha flux directly, it is not limited to a particular choice of ionizing background or mean transmitted flux.