  In the standard picture for low-mass star formation, a dense molecular cloud
undergoes gravitational collapse to form a protostellar system consisting of a
new central star, a circumstellar disk, and a surrounding envelope of remaining
material. The mass distribution of the system evolves as matter accretes from
the large-scale envelope through the disk and onto the protostar. While this
general picture is supported by simulations and indirect observational
measurements, the specific timescales related to disk growth and envelope
dissipation remain poorly constrained. In this paper we conduct a rigorous test
of a method introduced by J{\o}rgensen et al. (2009) to obtain mass
measurements of disks and envelopes around embedded protostars with
observations that do not resolve the disk (resolution of $\sim$1000\,AU). Using
unresolved data from the recent Mass Assembly of Stellar Systems and their
Evolution with the SMA (MASSES) survey, we derive disk and envelope mass
estimates for $59$ protostellar systems in the Perseus molecular cloud. We
compare our results to independent disk mass measurements from the VLA Nascent
Disk and Multiplicity (VANDAM) survey and find a strong linear correlation,
suggesting that accurate disk masses can be measured from unresolved
observations. Then, leveraging the size of the MASSES sample, we find no
significant trend in protostellar mass distribution as a function of age, as
approximated from bolometric temperatures. These results may indicate that the
disk mass of a protostar is set near the onset of the Class 0 protostellar
stage and remains roughly constant throughout the Class I protostellar stage.
