Assembling transition metal dichalcogenides (TMDCs) at the two-dimensional (2D) limit is a promising approach for tailoring emerging states of matter such as superconductivity or charge density waves (CDWs). Single-layer (SL) VSe$_2$ stands out in this regard because it exhibits a strongly enhanced CDW transition with a higher transition temperature compared to the bulk in addition to an insulating phase with an anisotropic gap at the Fermi level, causing a suppression of anticipated 2D ferromagnetism in the material. Here, we investigate the interplay of electronic and lattice degrees of freedom that underpin these electronic phases in SL VSe$_2$ using ultrafast pump-probe photoemission spectroscopy. In the insulating state, we observe a light-induced closure of the energy gap on a timescale of 480 fs, which we disentangle from the ensuing hot carrier dynamics. Our work thereby reveals that the phase transition in SL VSe$_2$ is driven by electron-lattice coupling and demonstrates the potential for controlling electronic phases in 2D materials with light.