Connecting the formation and evolution of galaxies to the large-scale structure is crucial for interpreting cosmological observations. While hydrodynamical simulations accurately model the correlated properties of galaxies, they are computationally prohibitive to run over volumes that match modern surveys. We address this by developing a framework to rapidly generate mock galaxy catalogs conditioned on inexpensive dark-matter-only simulations. We present a multi-modal, transformer-based model that takes 3D dark matter density and velocity fields as input, and outputs a corresponding point cloud of galaxies with their physical properties. We demonstrate that our trained model faithfully reproduces a variety of galaxy summary statistics and correctly captures their variation with changes in the underlying cosmological and astrophysical parameters, making it the first accelerated forward model to capture all the relevant galaxy properties, their full spatial distribution, and their conditional dependencies in hydrosimulations.