In this paper, we propose an extension to the approach of [Xi, C; et al. J. Chem. Theory Comput. 2022, 18, 6878] to calculate ion solvation free energies from first-principles (FP) molecular dynamics (MD) simulations of a hybrid solvation model. The approach is first re-expressed within the quasi-chemical theory of solvation. Then, to allow for longer simulation times than the original first-principles molecular dynamics approach and thus improve the convergence of statistical averages at a fraction of the original computational cost, a machine-learned (ML) energy function is trained on FP energies and forces and used in the MD simulations. The ML workflow and MD simulation times (≈200 ps) are adjusted to converge the predicted solvation energies within a chemical accuracy of 0.04 eV. The extension is successfully benchmarked on the same set of alkaline and alkaline-earth ions. The record includes all molecular-dynamics trajectories, energies and forces used to obtain the solvation energies of alkaline and alkaline-earth ions in water, as reported in Table 2 of referenced paper.