By virtue of the ultrashort phase-transition time of phase-change memory materials, e.g., Ge(2)Sb(2)Te(5), we successfully reproduce the early stages of crystallization in such a material using ab initio molecular-dynamics simulations. A stochastic distribution in the crystallization onset time is found, as generally assumed in classical nucleation theory. The critical crystal nucleus is estimated to comprise 5-10 (Ge,Sb)(4)Te(4) cubes. Simulated growth rates of crystalline clusters in amorphous Ge(2)Sb(2)Te(5) are consistent with extrapolated experimental measurements. The formation of ordered planar structures in the amorphous phase plays a critical role in lowering the interfacial energy between crystalline clusters and the amorphous phase, which explains why Ge-Sb-Te materials exhibit ultrafast crystallization.