  The first measurements of femtoscopic correlations with the particle pair
combinations $\pi^\pm$K$^0_{\rm S}$ in pp collisions at $\sqrt{s}=13$ TeV at
the Large Hadron Collider (LHC) are reported by the ALICE experiment. Using the
femtoscopic approach, it is shown that it is possible to study the elusive
K$^*_0(700)$ particle that has been considered a tetraquark candidate for over
forty years. Boson source parameters and final-state interaction parameters are
extracted by fitting a model assuming a Gaussian source to the experimentally
measured two-particle correlation functions. The final-state interaction is
modeled through a resonant scattering amplitude, defined in terms of a mass and
a coupling parameter, decaying into a $\pi^\pm$K$^0_{\rm S}$ pair. The
extracted mass and Breit-Wigner width, derived from the coupling parameter, of
the final-state interaction are found to be consistent with previous
measurements of the K$^*_0(700)$. The small value and increasing behavior of
the correlation strength with increasing source size support the hypothesis
that the K$^*_0(700)$ is a four-quark state, i.e. a tetraquark state. This
latter trend is also confirmed via a simple geometric model that assumes a
tetraquark structure of the K$^*_0(700)$ resonance.
