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 $dn/d\dot{M}$ 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 $z \lesssim 13\ (14)$. Comment: Published in ApJ, 16 pages, 12 figures, 3 tables
