The recent observation of the light-induced superconducting (SC)-like transient response in c-axis optical conductivity far above the SC transition temperature Tc in underdoped YBa2Cu3Oy (YBCO) has attracted a great deal of attention in the field of high-Tc superconductors. Since then, various theoretical and experimental studies have been devoted to elucidating its microscopic origin. One prominent fingerprint of light-induced superconductivity is the emergence of 1/ω-like spectral behavior in the imaginary part of the optical conductivity in the terahertz (THz) frequency range. However, the spectral profile can also be described by the Drude response of the quasiparticles (QPs) with a substantially low scattering rate. To circumvent this critical ambiguity, we investigated the light-induced nonequilibrium state in an underdoped YBCO sample with Tc of 61 K using the nonlinear THz optical response originating from the SC collective excitation of the ac-driven Josephson current. Upon the near-infrared (NIR) photoexcitation above Tc in the YBCO sample, the 1/ω-like spectral behavior in the imaginary part of the optical conductivity emerges, consistent with previous studies. However, the THz third-harmonic generation arising from the ac-driven Josephson current along the c-axis was absent in the NIR photoexcited state. These results indicate that the NIR pump-induced state exhibiting the 1/ω-like response above Tc is distinct from the long-range-ordered SC state in equilibrium. Based on these observations, the possible origins of the irregularly coherent charge-carrier response along the c-axis induced by photoexcitation are discussed.