  Due to their extremely dust-obscured nature, much uncertainty still exists
surrounding the stellar mass growth and content in dusty, star-forming galaxies
(DSFGs) at $z>1$. In this work, we present a numerical model built using
empirical data on DSFGs to estimate their stellar mass contributions across the
first $\sim$10 Gyr of cosmic time. We generate a dust-obscured stellar mass
function that extends beyond the mass limit of star-forming stellar mass
functions in the literature, and predict that massive DSFGs constitute as much
as $50-100\%$ of all star-forming galaxies with M $\ge10^{11}$M$_\odot$ at
$z>1$. We predict the number density of massive DSFGs and find general
agreement with observations, although more data is needed to narrow wide
observational uncertainties. We forward model mock massive DSFGs to their
quiescent descendants and find remarkable agreement with observations from the
literature demonstrating that, to first order, massive DSFGs are a sufficient
ancestral population to describe the prevalence of massive quiescent galaxies
at $z>1$. We predict that massive DSFGs and their descendants contribute as
much as $25-60\%$ to the cosmic stellar mass density during the peak of cosmic
star formation, and predict an intense epoch of population growth during the
$\sim1$ Gyr from $z=6$ to 3 during which the majority of the most massive
galaxies at high-$z$ grow and then quench. Future studies seeking to understand
massive galaxy growth and evolution in the early Universe should strategize
synergies with data from the latest observatories (e.g. JWST and ALMA) to
better include the heavily dust-obscured galaxy population.
