\justify Several methods have been developed to quantify the oceanic accumulation of anthropogenic carbon dioxide (CO$_2$) in response to rising atmospheric CO$_2$. Yet, we still lack a corresponding estimate of the changes in the total oceanic dissolved inorganic carbon (DIC). In addition to the increase in anthropogenic CO$_2$, changes in DIC also include alterations of natural CO$_2$. Once integrated globally, changes in DIC reflect the net oceanic sink for atmospheric CO$_2$, complementary to estimates of the air-sea CO$_2$ exchange based on surface measurements. Here, we extend the MOBO-DIC machine learning approach by \citeA{keppler_mapped_2020} to estimate global monthly fields of DIC at 1$^{\circ}$ resolution over the top 1500 m from 2004 through 2019. We find that over these 16 years and extrapolated to cover the whole global ocean down to 4000 m, the oceanic DIC pool increased close to linearly at an average rate of 3.2$\pm$0.7 Pg C yr$^{-1}$. This trend is statistically indistinguishable from current estimates of the oceanic uptake of anthropogenic CO$_2$ over the same period. Thus, our study implies no detectable net loss or gain of natural CO$_2$ by the ocean, albeit the large uncertainties could be masking it. Our reconstructions suggest substantial internal redistributions of natural oceanic CO$_2$, with a shift from the mid-latitudes to the tropics and from the surface to below $\sim$200 m. Such redistributions correspond with the Pacific Decadal Oscillation and the Atlantic Multidecadal Oscillation. The interannual variability of DIC is strongest in the tropical Western Pacific, consistent with the El Ni$\tilde{n}$o Southern Oscillation.