  We study the emergence of universal scaling in the time-evolving momentum
distribution of a harmonically trapped three-dimensional Bose-Einstein
condensate, parametrically driven to a turbulent state. We demonstrate that the
out-of-equilibrium dynamics post excitation is described by a single function
due to nearby non-thermal fixed points. The observed behavior connects the
dynamics of a quantum turbulent state to several far-from-equilibrium
phenomena. We present a controllable protocol to explore universality in such
systems, obtaining scaling exponents that can serve as reference for future
theoretical investigations. Our experimental results thus offer a promising
route to investigate the complex dynamics of the quantum turbulent regime under
a novel perspective.
