  We study quantum quench dynamics in the Fermi-Hubbard model, and its SU($N$)
generalizations, in one-dimensional lattices in the limit of infinite onsite
repulsion between all flavors. We consider families of initial states with
generalized Neel order, namely, initial state in which there is a periodic
$N$-spin pattern with consecutive fermions carrying distinct spin flavors. We
introduce an exact approach to describe the quantum evolution of those systems,
and study two unique transient phenomena that occur during expansion dynamics
in finite lattices. The first one is the dynamical emergence of Gaussian
one-body correlations during the melting of sharp (generalized) Neel domain
walls. Those correlations resemble the ones in the ground state of the SU($N$)
model constrained to the same spin configurations. This is explained using an
emergent eigenstate solution to the quantum dynamics. The second phenomenon is
the transformation of the quasimomentum distribution of the expanding strongly
interacting SU($N$) gas into the rapidity distribution after long times.
Finally, we study equilibration in SU($N$) gasses and show that observables
after equilibration are described by a generalized Gibbs ensemble. Our approach
can be used to benchmark analytical and numerical calculations of dynamics of
strongly correlated SU($N$) fermions at large $U$.
