The description of strongly correlated quantum many-body systems far from equilibrium presents a fundamental challenge due to the vast amount of information it requires. We introduce a generalization of the Jastrow ansatz for time-dependent wave functions that offers an efficient and exact description of the time evolution of various strongly correlated systems. Previously known exact solutions are characterized by scale invariance, enforcing self-similar evolution of local correlations, such as the spatial density. However, we demonstrate that a complex-valued time-dependent Jastrow ansatz (TDJA) is not restricted to scale invariance and can describe a broader class of dynamical processes lacking this symmetry. The associated time evolution is equivalent to the implementation of a shortcut to adiabaticity (STA) via counterdiabatic driving along a continuous manifold of quantum states described by a real-valued TDJA, providing a framework for engineering exact STA in strongly correlated many-body quantum systems. We illustrate our findings in systems with inverse-square interactions, such as the Calogero-Sutherland and hyperbolic models, supplemented with pairwise logarithmic interactions, as well as in the long-range Lieb-Liniger model, where bosons experience both contact and Coulomb interactions in one dimension. Our results enable the study of quench dynamics in all these models and serve as a benchmark for numerical and quantum simulations of nonequilibrium strongly correlated systems with continuous variables.