One of the main challenges in ultrafast material science is to trigger phase transitions with short pulses of light. Here we show how strain waves, launched by electronic and structural precursor phenomena, determine a coherent macroscopic transformation pathway for the semiconducting-to-metal transition in bistable Ti₃O₅ nanocrystals. Employing femtosecond powder X-ray diffraction, we measure the lattice deformation in the phase transition as a function of time. We monitor the early intra-cell distortion around the light absorbing metal dimer and the long range deformations governed by acoustic waves propagating from the laser-exposed Ti₃O₅ surface. We developed a simplified elastic model demonstrating that picosecond switching in nanocrystals happens concomitantly with the propagating acoustic wavefront, several decades faster than thermal processes governed by heat diffusion.