Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. The Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of charge gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time-dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed: 1) the recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and 2) the Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible–near-infrared domains.