We experimentally investigated the photoionization and fragmentation of a van der Waals cluster of argon dimer (${\mathrm{Ar}}_{2}$) exposed to intense laser fields. By performing femtosecond pump-probe experiments in a reaction microscope, we tracked the spatiotemporal evolution of the nuclear wave packet (NWP) launching onto the excited bound states of ${{\mathrm{Ar}}_{2}}^{+}$. By interrogating the measured time-resolved vibrational structures in the kinetic energy spectra obtained from Coulomb explosion imaging of the ${{\mathrm{Ar}}_{2}}^{+}$ NWP, the vibrational revival and rotational excitation of the long-living rovibrational NWP were observed in real time. The vibrational populations of the NWP on the potential curves of three excited bound states of ${{\mathrm{Ar}}_{2}}^{+}$, i.e., $I{(3/2)}_{g}, II{(1/2)}_{u}$, and $I{(3/2)}_{u}$, were identified by the Fourier analysis of the time-dependent kinetic energy spectra of nuclear fragments.