  We report measurements of the Meissner screening profile in a Nb(300
nm)/Al$_{2}$O$_{3}$ thin film using $^{8}$Li $\beta$-detected nuclear magnetic
resonance ($\beta$-NMR). The NMR probe $^{8}$Li was ion-implanted into the Nb
film at energies $\leq$ 20 keV, corresponding to mean stopping depths
comparable to Nb's magnetic penetration depth $\lambda$. $^{8}$Li's strong
dipole-dipole coupling with the host $^{93}$Nb nuclei provided a
"cross-relaxation" channel that dominated in low magnetic fields, which
conferred indirect sensitivity to the local magnetic field via the spin-lattice
relaxation (SLR) rate $1/T_{1}$. From a fit of the $1/T_{1}$ data to a model
accounting for its dependence on temperature, magnetic field, and
$^{8}$Li$^{+}$ implantation energy, we obtained a magnetic penetration depth
$\lambda_{0}$ = 51.5(22) nm, consistent with a relatively short carrier
mean-free-path $\ell$ = 18.7(29) nm typical of similarly prepared Nb films. The
results presented here constitute an important step towards using $^{8}$Li
$\beta$-NMR to characterize bulk Nb samples with engineered surfaces, which are
often used in the fabrication of particle accelerators.
