Phase-change materials show promising features for high-speed, non-volatile, random access memory, however achieving a fast electrical switching is a key challenge. We report here, the dependence of electrical switching dynamics including transient parameters such as delay time, switching time, etc., on the applied voltage and the set process of In3SbTe2 phase-change memory devices at the picosecond (ps) timescale. These devices are found to exhibit threshold-switching at a critical voltage called threshold-voltage, VT of 1.9 ± 0.1 V, having a delay time of 25 ns. Further, the delay time decreases exponentially to a remarkably smaller value, as short as 300 ± 50 ps upon increasing the applied voltage up to 1.1VT. Furthermore, we demonstrate a rapid phase-change behavior from amorphous (∼10 MΩ) to poly-crystalline (∼10 kΩ) phase using time-resolved measurements revealing an ultrafast set process, which is primarily initiated by the threshold-switching process within 550 ps for an applied voltage pulse with a pulse-width of 1.5 ns and an amplitude of 2.3 V.