The realization of quantum spin liquids on a triangular lattice magnet remains challenging due to quenched disorders present in real materials. Here, we report local-probe signatures of spin-liquid-like excitations in the structurally perfect triangular antiferromagnet ${\mathrm{Na}}_{2}\mathrm{BaCo}{({\mathrm{PO}}_{4})}_{2}$. Our zero-field and longitudinal-field muon spin relaxation measurements reveal both spatially and temporally correlated spins with no hint of static magnetism down to 80 mK, consistent with a quantum spin liquid. Comprehensive $^{23}\mathrm{Na}$ nuclear magnetic resonance experiments enable us to identify a field-induced crossover of magnetic excitations from a spinonlike to a gapped magnon at the critical field ${\ensuremath{\mu}}_{0}{H}_{C}=1.65$ T. Our findings uncover the temporal, thermal, and magnetic-field characteristics of the magnetic excitations in the triangular-lattice quantum spin liquid candidate ${\mathrm{Na}}_{2}\mathrm{BaCo}{({\mathrm{PO}}_{4})}_{2}$.