Organic lasers offer the promise to build compact, inexpensive, broadly tunable solid-state lasers in the visible range, with potential applications in spectroscopy, bio/chemo sensing or short-haul data telecommunications. Among existing laser architectures of optically-pumped organic lasers, external-cavity resonators enable the highest conversion efficiencies, excellent beam quality, power scalability and versatility due to the open cavity. Recently, we reported on an open-cavity laser architecture using a thin film of dye-doped polymer as the gain medium, named Vertical External Cavity Surface-emitting Organic Laser (VECSOL). The very high gain of organics make these lasers highly efficient even for macroscopic cavities, even though the pulse buildup time must be short enough to fit within the gain time window defined by the pump pulse duration and the fluorescence lifetime.In this paper we analyze the laser turn-on dynamics of organic VECSELs. A simple theoretical framework is presented, based on the Statz-DeMars coupled rate equations. Simulations are compared to the experimental pulse shapes of the pump and laser beams, recorded with the same fast photodiode. We observe that the laser pulse is both shifted and broadened with respect to the 0.5-ns-long pump pulse when the cavity length is increased, together with a drop of efficiency. Efficiency curves are presented, showing a higher threshold and lower slope efficiency when the cavity length increases, which is well accounted by the model. Finally, an optimized VECSOL is presented, with a 25 ns-pulsewidth pump source, enabling reaching conversion efficiencies up to 61%.