The existence and nature of a random singlet phase in higher dimensions remains elusive, despite certain theories and experiments alluding to its potential stability. In the frustrated cubic antiferromagnet La3Sb3Mn2O14, we identify a scaling relation in ac magnetic susceptibility and magnetization with a scaling exponent of 0.53, giving evidence for emergent random singlets rather than a spin glass. This finding extends the notion of a random-singlet state from low-dimensional quantum to three-dimensional S=5/2 frustrated spin systems.