The initialization of a resident hole spin by the absorption of a circularly polarized light at resonance involves the formation of an excited state called a trion state. For a pure heavy hole, this optical initialization is mediated by the hyperfine electron-nuclear coupling in the trion state. We show here that for a mixed-hole spin an additional mechanism for the optical initialization appears, associated to 'crossed transitions'; it becomes dominant and keeps a high level of hole spin polarization when the magnetic field screens the electron-nuclear interaction. Finally, using a simple model, we obtain a good theoretical agreement with pulsed pump-probe experiments.