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Proximity-induced long-range spin-triplet supercurrents, important for the field of superconducting spintronics, are generated in superconducting/ferromagnetic heterostructures when interfacial magnetic inhomogeneities responsible for spin mixing and spin flip scattering are present. The multilayer stack Nb/Cr/Fe/Cr/Nb has been shown to support such exotic currents when fabricated into Josephson junction devices. However, creating pure spin currents controllably in superconductors outside of the Josephson junction architecture is a bottleneck to progress. Recently, ferromagnetic resonance was proposed as a possible direction, the signature of pure supercurrent creation being an enhancement of the Gilbert damping below the superconducting critical temperature, but the necessary conditions are still poorly established. Consistent with theoretical prediction, we demonstrate conclusively that pumping pure spin currents into a superconductor is only possible when conditions supporting proximity-induced spin-triplet effects are satisfied. Our study is an important step forward for superconducting pure spin current creation and manipulation, considerably advancing the field of superconducting spintronics.