Quantum coherence is pivotal in various applications ranging from chemical control to quantum computing. An example of its manifestation in molecular dynamics is inversion symmetry breaking in the photodissociation of homonuclear diatomic molecules. On the other hand, the dissociative attachment of an incoherent electron also induces such coherent dynamics. However, these processes are resonant and occur for projectiles with a specific energy. Here we present the most general scenario of non-resonant inelastic electron scattering inducing such a quantum coherence in molecular dynamics. The ion-pair formation (H++ H─) that proceeds after the electron impact excitation of H2shows a forward-backward asymmetry about the incoming electron beam. Simultaneous transfer of multiple angular momentum quanta during the electron collision induces the underlying coherence in the system. The non-resonant nature of this process makes this effect generic and points to its possible prevalent role in particle collision processes, including electron-induced chemistry.