Class I protostars are thought to represent an early stage in the lifetime of protoplanetary disks, when they are still embedded in their natal envelope. Here we measure the disk masses of 10 Class I protostars in the Taurus Molecular Cloud to constrain the initial mass budget for forming planets in disks. We use radiative transfer modeling to produce synthetic protostar observations and fit the models to a multi-wavelength data set using a Markov Chain Monte Carlo fitting procedure. We fit these models simultaneously to our new Combined Array for Research in Millimeter-wave Astronomy 1.3 mm observations that are sensitive to the wide range of spatial scales that are expected from protostellar disks and envelopes so as to be able to distinguish each component, as well as broadband spectral energy distributions compiled from the literature. We find a median disk mass of 0.018 M☉ on average, more massive than the Taurus Class II disks, which have median disk mass of ∼0.0025 M☉. This decrease in disk mass can be explained if dust grains have grown by a factor of 75 in grain size, indicating that by the Class II stage, at a few Myr, a significant amount of dust grain processing has occurred. However, there is evidence that significant dust processing has occurred even during the Class I stage, so it is likely that the initial mass budget is higher than the value quoted here.