The study of the strength and behavior of the antikaon-nucleon (K[over ¯]N) interaction constitutes one of the key focuses of the strangeness sector in low-energy quantum chromodynamics (QCD). In this Letter a unique high-precision measurement of the strong interaction between kaons and protons, close and above the kinematic threshold, is presented. The femtoscopic measurements of the correlation function at low pair-frame relative momentum of (K^{+}p⊕K^{-}p[over ¯]) and (K^{-}p⊕K^{+}p[over ¯]) pairs measured in pp collisions at sqrt[s]=5, 7, and 13 TeV are reported. A structure observed around a relative momentum of 58  MeV/c in the measured correlation function of (K^{-}p⊕K^{+}p[over ¯]) with a significance of 4.4σ constitutes the first experimental evidence for the opening of the (K[over ¯]^{0}n⊕K^{0}n[over ¯]) isospin breaking channel due to the mass difference between charged and neutral kaons. The measured correlation functions have been compared to Jülich and Kyoto models in addition to the Coulomb potential. The high-precision data at low relative momenta presented in this work prove femtoscopy to be a powerful complementary tool to scattering experiments and provide new constraints above the K[over ¯]N threshold for low-energy QCD chiral models.