  The interaction of $\Lambda$ and $\Sigma$ hyperons (Y) with nucleons (N) is
strongly influenced by the coupled-channel dynamics. Due to the small mass
difference of the $\rm N \Lambda$ and $\rm N \Sigma$ systems, the sizeable
coupling strength of the $\rm N \Sigma\leftrightarrow N \Lambda$ processes
constitutes a crucial element in the determination of the N$\Lambda$
interaction. In this letter we present the most precise measurements on the
interaction of p$\Lambda$ pairs, from zero relative momentum up to the opening
of the $\rm N \Sigma$ channel. The correlation function in the relative
momentum space for
$\mathrm{p}\Lambda\oplus\overline{\mathrm{p}}\overline{\Lambda}$ pairs measured
in high-multiplicity triggered pp collisions at $\sqrt{s}~=~13$ TeV at the LHC
is reported. The opening of the inelastic N$\Sigma$ channels is visible in the
extracted correlation function as a cusp-like structure occurring at relative
momentum $k^{*}$ = 289 MeV/$c$. This represents the first direct experimental
observation of the $\rm N \Sigma\rightarrow N \Lambda$ coupled channel in the
p$\Lambda$ system. The correlation function is compared with recent chiral
effective field theory calculations, based on different strengths of the $\rm N
\Sigma\leftrightarrow N \Lambda$ transition potential. A weaker coupling, as
possibly supported by the present measurement, would require a more repulsive
three-body NN$\Lambda$ interaction for a proper description of the $\Lambda$
in-medium properties, which has implications on the nuclear equation of state
and for the presence of hyperons inside neutron stars.
