We demonstrate that a Bjorken expanding strongly coupled $\mathcal{N}=4$ Supersymmetric Yang-Mills plasma can display dynamically-driven violations of the dominant and also the weak energy condition during hydrodynamization. In addition, we find that a period of vanishing entropy production in far-from-equilibrium stages induces later violations of the dominant energy condition in the strongly coupled plasma. Such violations cannot occur in a classical description of hydrodynamization and suggest that the inclusion of quantum effects in transport can lead to new phenomena in these regimes, even for systems without anomalies or spin.