The atomic structure of glassy GeSe₃ is obtained via first-principles molecular dynamics (FPMD) calculations by employing a simulation cell of 480 atoms. We complement and improve results previously published (Ref. Micoulaut et al., (2013)) on a smaller system (120 atoms) characterized by a marked disagreement with neutron scattering experiments on the occurrence of Ge-Ge homonuclear bonds. The present calculations show that a finite number of Ge-Ge bonds may occur on specific trajectories depending on the initial conditions selected for the quench from the liquid state. This conclusion is substantiated by the observation that the first trajectory we produced resulted in a negligible number of such homonuclear bonds, while the second did feature some of them. In terms of tetrahedral connections (either edge-sharing or corner-sharing) FPMD results appear to overestimate the edge-sharing ones, the extent of the disagreement depending on the reference experimental probe employed for the comparison (neutron scattering or NMR).