In itinerant electronic systems, spontaneous symmetry breaking results from an interplay between interactions and density of states: a large density of states allows electrons to form long-range correlations by reducing the associated kinetic energy cost. The prospect of realizing new correlated states of electrons motivates us to seek methods for engineering band structures exhibiting large densities of states. We show that "Floquet engineering" via application of strong electromagnetic fields provides means for obtaining the necessary density of states to realize a novel non-equilibrium spontaneous symmetry breaking transition. We show that the transition occurs in the steady-state of the system achieved due to interplay between the coherent external drive, electron-electron interactions, and dissipative processes due to coupling to phonons and the electromagnetic environment. We obtain the phase diagram of the system using numerical calculations that match predictions obtained from a phenomenological treatment and discuss the conditions on the system and the external drive under which spontaneous symmetry breaking occurs. Our results imply that Floquet engineering of the density of states provides a new route for obtaining correlated states of electrons "on-demand".