In the literature, the experimental studies in laser-bound electron interaction without ionization show us that a specific amount of material-dependent response time must already pass so that the conventional interaction starts afterward and the bound electrons sense the electric field being applied to them. On the other hand, due to the lack of this conventional interaction in the mentioned material-specific response-time region, it is not correct to assume that the material is absolutely transparent to the applied field during this time period, in which we hypothesized that there must be an unconventional light-matter interaction phenomenon. We report the first numerical hypothesis for modeling the mechanism of this phenomenon, of which the interaction procedure has not yet been clearly understood. Our hypothesis very simply modifies the interaction Hamiltonian of the system by embedding an unknown time-varying function that we named the modifier function, proposing that it exists only in the response-time region of the material. The numerical solution in this study proved the existence of the modifier function in the response-time region for the first time. In our humble opinion, this proven phenomenon must be studied and understood more clearly both theoretically and experimentally for each material.