The slow $\beta$ relaxation is understood to be a universal feature of glassy dynamics. Its presence in bulk metallic glasses (BMGs) is evidence of a broad relaxation time spectrum that extends to deep within the glassy state. Despite the breadth of research devoted to this phenomenon, its microscopic origin is still not fully understood. The low-temperature aging behavior and atomic structural rearrangements of a ${\mathrm{Au}}_{49}$ ${\mathrm{Cu}}_{26.9}$ ${\mathrm{Si}}_{16.3}$ ${\mathrm{Ag}}_{5.5}$ ${\mathrm{Pd}}_{2.3}$ BMG are investigated in the regime of the slow $\beta$ relaxation by employing an ensemble of experimental techniques such as high-intensity synchrotron x-ray scattering, modulated differential scanning calorimetry (MDSC), dynamic mechanical analysis (DMA), impulse excitation, and dilatometry. Evidence of a distinct slow $\beta$-relaxation regime is seen in the form of (1) an excess wing of the DMA loss modulus beginning at $\sim$50 ${}^{\circ }$C, (2) a crossover effect of elastic modulus with isothermal aging at 50${}^{\circ }$C, and (3) a broad, nonreversing and largely irreversible sub-$T_g$ endotherm in the MDSC results. Atomic rearrangements occurring at the onset of the measured slow $\beta$-relaxation temperature regime were found to be confined mainly to the short-range order length scale while no significant atomic rearrangements occur on the length scale of the medium-range order. Furthermore, evidence is presented that suggests the crossover effect in Young's modulus is due to the evolution of chemical short-range order. These results support the emergent picture of a dynamically heterogeneous glassy structure, in which low-temperature relaxation occurs through atomic rearrangements confined mostly to the short-range order length scale.