  Within the model A in the Hohenberg's dynamical universality classification,
we investigate the critical slowing down effects on the critical fluctuations
driven by the expanding quark-gluon plasma, using a trajectory and cooling rate
obtained from hydrodynamics. We numerically solved the Langevin dynamics of the
non-conserved order parameter field and find that, compared with commonly used
Hubble-like expansion, the cooling rate of a realistic hydrodynamic system is
pretty large and the associated critical slowing down effects strongly suppress
the higher-order cumulants of the order parameter field ({\it e.g.,} $C_4$).
Furthermore, for an evolving system that approaches the critical point, such
critical slowing down suppression overcomes the enhancement of the critical
fluctuations, which indicates that the largest fluctuations of the order
parameter field ({\it i.e.,} $C_2$) do not necessarily associate with the
evolving trajectory closest to the critical point.
