The volatile composition of a planet is determined by the inventory of gas and ice in the parent disk. The volatile chemistry in the disk is expected to evolve over time, though this evolution is poorly constrained observationally. We present Atacama Large Millimeter/submillimeter Array observations of (CO)-O-18, C2H, and the isotopologues (HCN)-C-13, (HCN)-N-15, and DCN toward five Class 0/I disk candidates. Combined with a sample of 14 Class II disks presented in Bergner et al., this data set offers a view of volatile chemical evolution over the disk lifetime. Our estimates of (CO)-O-18 abundances are consistent with a rapid depletion of CO in the first similar to 0.5-1 Myr of the disk lifetime. We do not see evidence that C2H and HCN formation are enhanced by CO depletion, possibly because the gas is already quite under-abundant in CO. Further CO depletion may actually hinder their production by limiting the gas-phase carbon supply. The embedded sources show several chemical differences compared to the Class II stage, which seem to arise from shielding of radiation by the envelope (impacting C2H formation and (HCN)-N-15 fractionation) and sublimation of ices from infalling material (impacting HCN and (CO)-O-18 abundances). Such chemical differences between Class 0/I and Class II sources may affect the volatile composition of planet-forming material at different stages in the disk lifetime.