We present an ab initio study of the correlation between nuclear matrix elements (NMEs) of 0⁢𝜈⁢𝛽⁢𝛽 decay and nucleon-nucleon scattering phase shifts in the 1 𝑆 0 channel. Starting from 34 statistically weighted interactions derived from chiral effective field theory, we apply the valence-space in-medium similarity renormalization group to calculate NMEs in the four experimentally relevant isotopes. Comparing with the 1 𝑆 0 -channel phase shifts given from each interaction, in all cases we observe a strong correlation for scattering energies above approximately 75 MeV. From a global sensitivity analysis, enabled by newly developed machine-learning emulators, we find that 0⁢𝜈⁢𝛽⁢𝛽 NMEs indeed depend primarily on the 𝐶1⁢𝑆⁢0 low-energy constant, which is associated with phase shifts in that partial wave. These results provide the first clear correlation between 0⁢𝜈⁢𝛽⁢𝛽 decay NMEs and a measured observable, and have already been shown to reduce the total uncertainty of the NME in 76 Ge by ≈25%. This correlation will serve as a crucial component in ongoing and future refinements of ab initio uncertainty estimates for 0⁢𝜈⁢𝛽⁢𝛽 decay.