This study theoretically investigates a dynamic process of periodic structures formed on a gold surface through a single-pulse laser, to discuss the transient changes during the formation of laser-induced periodic surface structure (LIPSS). We employ the two-temperature model to calculate the electron and lattice temperatures of the gold surface and use the excited-state dielectric constant to determine the transient optical properties after laser irradiation. We explore the relationships between the refractive index, extinction coefficient, scattering frequency, and LIPSS period. Results reveal fluctuations in the optical properties, electron-electron scattering frequency, electron-phonon scattering frequency, and LIPSS period following laser action. The theoretical predictions align closely with experimental observations reported in the literature. Notably, the extinction coefficient and electron-electron scattering frequency significantly influence the LIPSS period compared to the refractive index and electron-phonon scattering frequency. The time evolution of the LIPSS period after femtosecond laser action is accurately predicted by the surface plasmon polaritons model based on the excited-state dielectric constant.