  We study the quench dynamics of a two dimensional superconductor in a lattice
of size up to $200\times 200$ employing the self-consistent time dependent
Bogoliubov-de Gennes (BdG) formalism. In the clean limit, the dynamics of the
order parameter for short times, characterized by a fast exponential growth and
an oscillatory pattern, agrees with the Bardeen-Cooper-Schrieffer (BCS)
prediction. However, unlike BCS, we observe for longer times an universal
exponential decay of these time oscillations that we show explicitly to be
induced by the full emergence of spatial inhomogeneities of the order
parameter, even in the clean limit, characterized by the exponential growth of
its variance. The addition of a weak disorder does not alter these results
qualitatively. In this region, the spatial inhomogeneities rapidly develops
into an intricate spatial structure consisting of ordered fragmented stripes in
perpendicular directions where the order parameter is heavily suppressed
especially in the central region. As the disorder strength increases, the
fragmented stripes gradually turn into a square lattice of approximately
circular spatial regions where the condensate is heavily suppressed. A further
increase of disorder leads to the deformation and ultimate destruction of this
lattice. We explore suitable settings for the experimental confirmation of
these findings.
