  We report the realization of a strong coupling between a Gd$^{3+}$ spin
ensemble hosted in a scheelite (CaWO$_4$) single crystal and the resonant mode
of a coplanar stripline superconducting cavity leading to a large separation of
spin-photon states of 146 MHz. The interaction is well described by the Dicke
model and the crystal-field Hamiltonian of the multilevel spin system. We
observe a change of the crystal-field parameters due to the presence of photons
in the cavity that generates a significant perturbation of the crystal ground
state. Using finite-element calculations, we numerically estimate the cavity
sensing volume as well as the average spin-photon coupling strength of
$g_0\approx$ 620 Hz. Lastly, the dynamics of the spin-cavity states are
explored via pulsed measurements by recording the cavity ring-down signal as a
function of pulse length and amplitude. The results indicate a potential method
to initialize this multilevel system in its ground state via an active cooling
process.
