In triangular lattice structures, spatial anisotropy and frustration can lead to rich equilibrium phase diagrams with regions containing complex, highly entangled states of matter. In this work, we study the driven two-rung triangular Hubbard model and evolve these states out of equilibrium, observing how the interplay between the driving and the initial state unexpectedly shuts down the particle-hole excitation pathway. This restriction, which symmetry arguments fail to predict, dictates the transient dynamics of the system, causing the available particle-hole degrees of freedom to manifest uniform long-range order. We discuss implications of our results for a recent experiment on photoinduced superconductivity in κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Br molecules.