CePdAl is a prototypical frustrated Kondo lattice with partial long-range order (LRO) at TN=2.7 K. Previous bulk experiments under hydrostatic pressure found signatures for a quantum critical regime that extends from pc≈0.9 GPa, where LRO disappears, up to ∼1.7 GPa. We employed extensive muon spin relaxation and rotation experiments under pressure. The continuous and complete suppression of LRO at pc is confirmed. Above TN(p) and beyond pc, an additional crossover scale T∗(p) characterizes the change from pure to stretched exponential relaxation in zero field. Remarkably, T∗(p) agrees with previously determined signatures of entropy accumulation above LRO. This coincidence microscopically evidences fluctuating frustrated spins at T≤T∗ with spin-liquid behavior. Power-law divergences of the temperature and longitudinal field dependences of the relaxation rate, with time-field scaling, at pressures between pc and 1.7 GPa characterize this regime as quantum critical. © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.