SCORCH (Simulations and Constructions of the Reionization of Cosmic Hydrogen) is a new project to study the Epoch of Reionization (EoR). In this first paper, we probe the connection between observed high-redshift galaxies and simulated dark matter halos to better understand the abundance and evolution of the primary source of ionizing radiation. High-resolution N-body simulations are run to quantify the abundance of dark matter halos as a function of mass $M$, accretion rate $dot{M}$, and redshift $z$. A new fit for the halo mass function $dn/dM$ is $approx 20%$ more accurate at the high-mass end where bright galaxies are expected to reside. A novel approach is used to fit the halo accretion rate function $dn/ddot{M}$ in terms of the halo mass function. Abundance matching against the observed galaxy luminosity function is used to estimate the luminosity-mass relation and the luminosity-accretion-rate relation. The inferred star formation efficiency is not monotonic with $M$ nor $dot{M}$, but reaches a maximum value at a characteristic mass $sim 2 times 10^{11} M_odot$ and a characteristic accretion rate $sim 6 times 10^2 M_odot/{rm yr}$ at $z approx 6$. We find a universal EoR luminosity-accretion-rate relation and construct a fiducial model for the galaxy luminosity function. The Schechter parameters evolve such that $phi_star$ decreases, $M_star$ is more positive (fainter), and $alpha$ is more negative (steeper) at higher redshifts. We forecast for the upcoming James Webb Space Telescope and show that with apparent magnitude limit $m_{rm AB} approx 31 (32)$, it can observe $gtrsim 11 (24)$ unlensed galaxies per square degree per unit redshift at least down to $M_star$ at $z lesssim 13 (14)$.
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