Inverse magnetostriction is the effect by which magnetization can be changed upon application of stress/strain. A strain modulation may be created electrically by exciting interdigitated transducers to generate surface acoustic waves (SAWs). Hence SAWs appear as a possible route towards induction-free undulatory magnetic data manipulation. Here we demonstrate experimentally on an out-of-plane magnetostrictive layer a reduction of the coercive field of up to 60% by a SAW, over millimetric distances. A simple model shows that this spectacular effect can be partly explained by the periodic lowering of the strain-dependent domain nucleation energy by the SAW. This proof of concept was done on (Ga,Mn)(As,P), a magnetic semiconductor in which the out-of-plane magnetic anisotropy can be made very weak by epitaxial growth; it should guide material engineering for all-acoustic magnetization switching.