  Motivated by the report of superconductivity in bilayer La$_3$Ni$_2$O$_7$ at
high pressure, we examine the interacting electrons in this system.
First-principles many-body theory is utilized to study the normal-state
electronic properties. Below 100\,K, a multi-orbital non-Fermi liquid state
resulting from loss of Ni-ligand coherence within a flat-band dominated
low-energy landscape is uncovered. The incoherent low-temperature Fermi surface
displays strong mixing between Ni-$d_{z^2}$ and Ni-$d_{x^2-y^2}$ orbital
character. In a model-Hamiltonian picture, spin fluctuations originating mostly
from the Ni-$d_{z^2}$ orbital give rise to strong tendencies towards a
superconducting instability with $B_{1g}$ or $B_{2g}$ order parameter. The
dramatic enhancement of $T_{\rm c}$ in pressurized La$_3$Ni$_2$O$_7$ is due to
stronger Ni-$d_{z^2}$ correlations compared to those in the infinite-layer
nickelates.
