A contending technology for nonvolatile memories of the next generation is based on a remarkable property of chalcogenide alloys known as phase change materials, namely their ability to undergo a fast and reversible transition between the amorphous and crystalline phases upon heating. The fast crystallization has been ascribed to the persistence of a high atomic mobility in the supercooled liquid phase, down to temperatures close to the glass transition. In this work we unravel the atomistic, structural origin of this feature in the supercooled liquid state of GeTe, a prototypical phase change compound, by means of molecular dynamic simulations. To this end, we employed an interatomic potential based on a neural network framework, which allows simulating thousands of atoms for tens of ns by keeping an accuracy close to that of the underlying first-principles framework. Our findings demonstrate that the high atomic mobility is related to the presence of clusters of slow and fast moving atoms. The latter contain a large fraction of chains of homopolar GeGe bonds, which at low temperatures have a tendency to move by discontinuous cage-jump rearrangements. This structural fingerprint of dynamical heterogeneity provides an explanation of the breakdown of the StokesEinstein relation in GeTe, which is the ultimate origin of the fast crystallization of phase change materials exploited in the devices.