Glass-forming materials are employed in information storage technologies making use of the transition between a disordered (amorphous) and an ordered (crystalline) state. With increasing temperature, the crystal growth velocity of these phase-change materials becomes so fast that prior studies have not been able to resolve these crystallization dynamics. However, crystallization is the time-limiting factor in the write speed of phase-change memory devices. Here, for the first time, we quantify crystal growth velocities up to the melting point using the relaxation of photoexcited carriers as an ultrafast heating mechanism. During repetitive femtosecond optical excitation, each pulse enables dynamical evolution for tens of picoseconds before the intermediate atomic structure is frozen-in as the sample rapidly cools. We apply this technique to $Ag_{4}In_{3}Sb_{67}Te_{26}$ (AIST) and compare the dynamics of as-deposited and application-relevant melt-quenched glass. Both glasses retain their different kinetics even in the supercooled liquid state, thereby revealing differences in their kinetic fragilities. This approach enables the characterization of application-relevant properties of phase-change materials up to the melting temperature, which has not been possible before.