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Atomistic simulations can offer direct access to the atomic structure of glasses, which is otherwise invisible from conventional experiments. However, molecular dynamics (MD) simulations of glasses based on the melt-quenching technique remain plagued by the use of high cooling rates, while reverse Monte Carlo (RMC) modeling can yield non-unique solutions. Here, we adopt the force-enhanced atomic refinement (FEAR) method to overcome these limitations and decipher the atomic structure of a sodium silicate glass. We show that FEAR offers an unprecedented description of the atomic structure of sodium silicate, wherein the simulated configuration simultaneously exhibits enhanced agreement with experimental diffraction data and higher energetic stability as compared to those generated by MD or RMC. This result allows us to reveal new insights into the atomic structure of sodium silicate glasses. Specifically, we show that sodium silicate glasses exhibit a more ordered medium-range order structure than previously suggested by MD simulations. These results pave the way toward an increased ability to accurately describe the atomic structure of glasses.