  We study the dynamics and timescales of a periodically driven Fermi-Hubbard
model in a three-dimensional hexagonal lattice. The evolution of the Floquet
many-body state is analyzed by comparing it to an equivalent implementation in
undriven systems. The dynamics of double occupancies for the near- and
off-resonant driving regime indicate that the effective Hamiltonian picture is
valid for several orders of magnitude in modulation time. Furthermore, we show
that driving a hexagonal lattice compared to a simple cubic lattice allows to
modulate the system up to 1~s, corresponding to hundreds of tunneling times,
with only minor atom loss. Here, driving at a frequency close to the
interaction energy does not introduce resonant features to the atom loss.
