  We use infinite matrix-product-state techniques to study the time evolution
of the charge-density-wave (CDW) order after a quench or a light pulse in a
fundamental fermion-boson model. The motion of fermions in the model is linked
to the creation of bosonic excitations, which counteracts the melting of the
CDW order. For low-energy quenches corresponding to a change of the boson
relaxation rate, we find behavior similar to that in an effective $t$-$V$
model. When the boson energy is quenched instead or a light pulse is applied to
the system, the transient dynamics are more complex, with the CDW order first
quickly decreasing to an intermediate value while the density-wave-like order
of the bosons rises. In the case of pulse irradiation, the subsequent
time-evolution of the CDW order depends strongly on the photon frequency. For
frequencies slightly below the boson energy, we observe a temporary increase of
the CDW order parameter. Our results reveal the complex physics of driven Mott
insulators in low-dimensional systems with strong correlations.
