Manipulating materials properties far from equilibrium recently garnered significant attention, with experimental emphasis on transient melting, enhancement, or induction of electronic order. A more tantalizing aspect of the matter-light interaction regards the possibility to access dynamical steady states with distinct non-equilibrium phase transitions to affect electronic transport. Here, we show that the interplay of crystal symmetry and optical pumping of monolayer transition-metal dichalcogenides (TMDCs) provides a novel avenue to engineer topologically-protected chiral edge modes. In stark contrast to graphene and previously-discussed toy models, the underlying generic mechanism relies on the intrinsic three-band nature of TMDCs near the band edges. Photo-induced band inversions scale linearly in applied pump field and exhibit a transition from one to two chiral edge modes upon sweeping from red to blue detuning. We develop a strategy to understand non-equilibrium Floquet-Bloch bands and topological transitions directly from ab initio calculations, and illustrate for the example of WS2 that control of chiral edge modes can be dictated solely from symmetry principles and is not qualitatively sensitive to microscopic materials details. Show Partial Abstract