The Kohn-Luttinger (KL) mechanism of pairing, which describes superconductivity emergent from repulsive interactions, typically yields Cooper pairs at high angular-momentum (
ℓ>0) and extremely low transition temperatures (
Tc). Here, we reveal an inter-layer s-wave (
ℓ=0) KL superconductivity with greatly elevated
Tc in a multi-layer Hubbard model, which prototypes stacked two-dimensional (2D) electrons in layered van der Waals materials. By employing determinant quantum Monte Carlo and dynamical mean-field theory simulations, we show that a strong pairing attraction
V∗, without the mediation of collective modes, can emerge between inter-layer electrons in the system. As inter-layer repulsion
U increases,
V∗ evolves from a conventional KL relation of
V∗∝−U2, to a linear strong-coupling scaling of
V∗∝−U, resulting in enhanced superconductivity at large
U. This strong-coupling KL pairing is robust against changes in lattice geometries and dimensionalities, and it can persist, in the presence of a large remnant Coulomb repulsion
U∗ between pairing electrons. Using \textit{ab initio} calculations, we propose a few 2D layered van der Waals materials that can potentially realize and control this unconventional superconductivity.