While cosmological dark matter-only simulations relying solely on gravitational effects are comparably fast to compute, baryonic properties in simulated galaxies require complex hydrodynamic simulations that are computationally costly to run. We explore the merging of an extended version of the equilibrium model, an analytic formalism describing the evolution of the stellar, gas, and metal content of galaxies, into a machine learning framework. In doing so, we are able to recover more properties than the analytic formalism alone can provide, creating a high-speed hydrodynamic simulation emulator that populates galactic dark matter haloes in N-body simulations with baryonic properties. While there exists a trade-off between the reached accuracy and the speed advantage this approach offers, our results outperform an approach using only machine learning for a subset of baryonic properties. We demonstrate that this novel hybrid system enables the fast completion of dark matter-only information by mimicking the properties of a full hydrodynamic suite to a reasonable degree, and discuss the advantages and disadvantages of hybrid versus machine learning-only frameworks. In doing so, we offer an acceleration of commonly deployed simulations in cosmology.