As understanding experimentally observed two-dimensional electronic spectroscopy (2DES) signals usually requires theoretical modeling, various approaches have been applied to simulating the spectra. It will be desirable to develop a method that is free from parameters that are adjusted based on spectroscopic outcomes. Often, such parameters without any a priori known information come from quantum chemical calculations that can only be achieved at the atomistic resolution, and a necessity arises for designing a scheme that can be readily used for generating 2DES spectra even for atomistic models of complex systems. Here, we present such an approach based on mixed quantum-classical Poisson bracket mapping equation formalism, which can be extended to all-atom simulations. We check its performance by adopting a two-state toy model and show that we can efficiently construct 2D spectra. We show that our scheme can yield reasonable 2D spectra even when high-frequency vibrations modulate the population dynamics.