During the first billion years after the big bang, the large-scale cosmic web of structures we see today began to form. This was followed by the first stars and galaxies, which brought an end to the Dark Ages. These first luminous sources are thought to be the prime candidates which fuelled cosmic reionization, the last major phase transition of the Universe, from a neutral inter-galactic medium following recombination to the ionized state it remains in today. The physical processes which drive reionization encapsulate several areas of research, from cosmology and galaxy formation to radiative transfer and atomic physics. Even with the wealth of present-day observational information at our disposal, the processes are still not fully understood. Therefore we cannot model reionization analytically, instead turning to numerical simulations using observations to constrain our models. We perform a suite of fully-coupled radiation-hydrodynamical simulations of galaxy formation in cosmological volumes to probe the self-feedback of galaxies during the Epoch of Reionization. This research focuses on the transport of gas from the intergalactic medium onto dark matter halos, and consequences for semi-analytical models of galaxy formation. To improve on existing methods, which constrain the halo baryon fraction during reionization, we develop and train an artificial neural network to predict this quantity based on the physical properties of haloes. We demonstrate that this model is independent of redshift and reionization history, and can be trivially incorporated into semi-analytical models of galaxy formation. We further probe the physical processes which allow ionizing photons to escape from galaxies to reionize the Universe, specifically how stellar evolution uncertainties such as binary populations influence this process. Finally, we investigate to what extent a relative supersonic drift velocity between baryons and dark matter, present at recombination, may suppress the formation of the first objects and fundamentally alter their evolution. To do this, we develop a new method based on cosmological zoom simulations to include this effect in boxes much larger than the coherence length of the relative velocity for the first time.