  We study the stress tensor multiplet four-point function in the 3d maximally
supersymmetric ABJ(M) theory with Chern-Simons level $k=2$, which in the large
$N$ limit is holographically dual to weakly coupled M-theory on $AdS_4\times
S^7/\mathbb{Z}_2$. We use the Lorentzian inversion to compute the 1-loop
correction to this holographic correlator coming from Witten diagrams with
supergravity $R$ and the first higher derivative correction $R^4$ vertices, up
to a finite number of contact terms that contribute to low spins where the
inversion formula does not converge. We find a precise match with the
corresponding terms in the 11d M-theory S-matrix by taking the flat space
limit, which is not sensitive to these contact terms. We then conjecturally fix
these contact terms by analytically continuing the inversion formula below its
expected range of convergence, and verify this conjecture using supersymmetric
localization. Finally, we compare some of the 1-loop CFT data to
non-perturbative in $N$ bounds from the numerical conformal bootstrap, which we
compute at unprecedently high accuracy, and find that the 1-loop corrections
saturate the bounds in the large $N$ regime, which extends the previously
observed match at tree level.
