In this work, we present a candidate material, NaYbO<sub>2</sub>, that realizes the genuine spin-liquid state on the triangular lattice and benchmarks recent theoretical predictions on the relevant spin models. Synchrotron x-ray diffraction and neutron scattering exclude both structural disorder and crystal-electric-field randomness. Furthermore, our thermodynamic measurements, neutron diffraction, and muon spectroscopy coincidentally prove the absence of magnetic order and persistent spin dynamics down to at least 70 mK. Continuous magnetic excitations first observed by inelastic neutron scattering show a gapless feature and the low-energy spectral weight accumulating at the K point of the Brillouin zone, in agreement with theoretical predictions for the spin-liquid phase of triangular antiferromagnets. Such a gapless spin-liquid phase is further confirmed by our magnetic specific heat analysis that reveals a departure from simple power-law behavior. Our work demonstrates that NaYbO<sub>2</sub> practically gives direct experimental access to the spin-liquid physics of triangular antiferromagnets.