  Two decades of effort have been poured into both single-dish and
interferometric millimeter-wave surveys of the sky to infer the volume density
of dusty star-forming galaxies (DSFGs, with SFR>100M$_\odot$ yr$^{-1}$) over
cosmic time. Though obscured galaxies dominate cosmic star-formation near its
peak at $z\sim2$, the contribution of such heavily obscured galaxies to cosmic
star-formation is unknown beyond $z\sim2.5$ in contrast to the well-studied
population of Lyman-break galaxies (LBGs) studied through deep, space- and
ground-based pencil beam surveys in the near-infrared. Unlocking the volume
density of DSFGs beyond $z>3$, particularly within the first 1 Gyr after the
Big Bang is critical to resolving key open questions about early Universe
galaxy formation: (1) What is the integrated star-formation rate density of the
Universe in the first few Gyr and how is it distributed among low-mass galaxies
(e.g. Lyman-break galaxies) and high-mass galaxies (e.g. DSFGs and quasar host
galaxies)? (2) How and where do the first massive galaxies assemble? (3) What
can the most extreme DSFGs teach us about the mechanisms of dust production
(e.g. supernovae, AGB stars, grain growth in the ISM) <1 Gyr after the Big
Bang? We summarize the types of observations needed in the next decade to
address these questions.
