Nuclear matrix elements (NMEs) in double-beta decay are crucial for probing the nature of neutrinos. While they can, in principle, be inferred from experimental observables through nuclear reactions such as double-charge exchange, single-charge exchange, and two-nucleon transfer, sufficient precision has not yet been achieved. In this work, we present an alternative approach that introduces two complete sets of $(A-1)$-nucleon states and a complete set of $A$-nucleon states. This formulation directly links NMEs to one-nucleon transfer amplitudes, which are experimentally more accessible than in existing proposals. Using $^{48}$Ca as a proof-of-principle example, we find that, although many virtual states are involved, only a few low-energy states make substantial contributions. We also demonstrate that the available experimental data can
provide meaningful validation of the shell-model valence spaces. This approach offers a promising avenue for improving theoretical descriptions of double-beta decay and future experimental efforts.