Random lasers are a type of lasers that lack typical resonator structures, offering benefits such as easy integration, low cost, and low spatial coherence. These features make them popular for speckle-free imaging and random number generation. However, due to their high threshold and phase instability, the production of picosecond random lasers has still been a challenge. In this work, we have developed three dyes incorporating polymer optical fibers doped with various scattering nanoparticles to produce short-pulsed random fiber lasers. Notably, stable picosecond random laser emission lasting 600 ps is observed at a low pump energy of 50 µJ, indicating the gain-switching mechanism. Population inversion and gain undergo an abrupt surge as the intensity of the continuously pumped light nears the threshold level. When the intensity of the continuously pumped light reaches a specific value, the number of inversion populations in the “scattering cavity” surpasses the threshold rapidly. Simulation results based on a model that considers power-dependent gain saturation confirmed the above phenomenon. This research helps expand the understanding of the dynamics behind random medium-stimulated emission in random lasers and opens up possibilities for mode locking in these systems.