The time-averaged spectral function plays a central role in studying the Floquet properties of the many-body fermionic systems. Here, we study the time-averaged spectral function of the periodically driven bosonic systems by providing an exact and rigorous analysis in the strongly interacting one-dimensional limit. The exact analysis reveals that the nonequilibrium Lieb excitations emerge if the underlying steady states form a Floquet-Fermi sea. In the low-frequency limit, we find characteristic linear Lieb excitations that hybridize with Floquet-replica states in the second Floquet–Brillouin zone.