The Earth's deep interior contains significant reservoirs of volatiles such as H, C, and N. Due to the incompatible nature of these volatile species, it has been difficult to reconcile their storage in the residual mantle immediately following crystallization of the terrestrial magma ocean (MO). As the magma ocean freezes, it is commonly assumed that very small amounts of melt are retained in the residual mantle, limiting the trapped volatile concentration in the primordial mantle. In this article, we show that inefficient melt drainage out of the freezing front can retain large amounts of volatiles hosted in the trapped melt in the residual mantle while creating a thick early atmosphere. Using a two‐phase flow model, we demonstrate that compaction within the moving freezing front is inefficient over time scales characteristic of magma ocean solidification. We employ a scaling relation between the trapped melt fraction, the rate of compaction, and the rate of freezing in our magma ocean evolution model. For cosmochemically plausible fractions of volatiles delivered during the later stages of accretion, our calculations suggest that up to 77% of total H2O and 12% of CO2 could have been trapped in the mantle during magma ocean crystallization. The assumption of a constant trapped melt fraction underestimates the mass of volatiles in the residual mantle by more than an order of magnitude. Plain Language Summary The Earth's deep interior contains substantial amounts of volatile elements like C, H, and N. How these elements got sequestered in the Earth's interior has long been a topic of debate. It is generally assumed that most of these elements escaped the interior of the Earth during the first few hundred thousand years to create a primitive atmosphere, leaving the mantle reservoir nearly empty. In this work, we show that the key to this paradox involves the very early stages of crystallization of the mantle from a global magma ocean. Using numerical models, we show that the mantle stored substantially higher amounts of volatiles than previously thought, thanks to large quantities of melt trapped in the mantle due to rapid freezing of the magma ocean. Our models show that up to 77% of the total planetary budget of water and 12% of CO2 can be stored in the mantle due to this previously unaccounted process. Key Points Magma ocean freezing fronts retain more melt than previously thought Melt thus retained in the residual mantle can dissolve substantial amount of volatiles Following solidification of the magma ocean, the residual mantle can contain substantially larger amount of volatiles