When metallic glasses (MGs) are subjected to mechanical loads, the plastic response of atoms is non-uniform. However, the extent and manner in which atomic environment signatures present in the undeformed structure determine this plastic heterogeneity remain elusive. Here, we demonstrate that novel site environment features that characterize interstice distributions around atoms combined with machine learning (ML) can reliably identify plastic sites in several Cu-Zr compositions. Using only quenched structural information as input, the ML-based plastic probability estimates ("quench-in softness" metric) can identify plastic sites that could activate at high strains, losing predictive power only upon the formation of shear bands. Moreover, we reveal that a quench-in softness model trained on a single composition and quench rate substantially improves upon previous models in generalizing to different compositions and completely different MG systems (Ni62Nb38, Al90Sm10 and Fe80P20). Our work presents a general, data-centric framework that could potentially be used to address the structural origin of any site-specific property in MGs.