How do quantum many-body systems evolve when driven far from equilibrium? This theoretical internship explores this fundamental question in spin-orbit-coupled Bose gases, a remarkable platform hosting both superfluid and supersolid phases. By studying domain formation and coarsening following a quantum quench, the project aims to uncover the universal scaling laws and associated non-thermal fixed points characterizing the far-from-equilibrium physics of this system. Combining theoretical approaches and classical-field simulations, this work will pave the way towards understanding the formation and dynamics of quantum supersolids. The internship will take place in the stimulating research environment of the Laboratoire Kastler Brossel, with close interactions between theorists and experimentalists.