  The recent discovery of high-temperature superconductivity in $\mathrm{La}_3
\mathrm{Ni}_2 \mathrm{O}_7$ offers a fresh platform for exploring
unconventional pairing mechanisms. Based on a single-orbital bilayer model with
intralayer hopping $t_{\|}$ and interlayer super-exchange $J_{\perp}$, we
investigate the impact of the on-site Hubbard interaction $U$ in the Ni-3d
orbital on the binding strength of Cooper pairs. By extensive density matrix
renormalization group calculations, we observe a remarkable enhancement in
binding energy as much as $10$-$20$ times larger with $U/t_\|$ increasing from
$0$ to $12$ at $J_{\perp}/t_\|\sim 1$. We demonstrate that such a substantial
enhancement stems from a kinetic-energy-driven mechanism. Specifically, a
$\mathbb{Z}_2$ Berry phase will emerge at large $U$ due to the Hilbert space
restriction (Mottness), which strongly suppresses the mobility of single
particle propagation as compared to $U=0$. However, the kinetic energy of the
electrons (holes) can be greatly restored by forming an interlayer spin-singlet
pairing, which naturally results in a superconducting state even for relatively
small $J_\perp$. An effective hard-core bosonic model is further proposed to
provide an estimate for the superconducting transition temperature at the
mean-field level.
