The breakdown of the N=20 magic number in the so-called island of inversion around Mg-32 is well established. Recently developed large-scale shell-model calculations suggest a transitional region between normal- and intruder-dominated nuclear ground states, thus modifying the boundary of the island of inversion. In particular, a dramatic change in single-particle structure is predicted between the ground states of Mg-30 and Mg-32, with the latter consisting nearly purely of 2p-2h N=20 cross-shell configurations. Single-neutron knockout experiments on Mg-30,Mg-32 projectiles have been performed. We report on a first direct observation of intruder configurations in the ground states of these very neutron-rich nuclei. Spectroscopic factors to low-lying negative-parity states in the knockout residues are deduced and compare well with shell-model predictions.