In this work, we observe natural exceptional points in the excitation spectrum of an exciton–polariton system by optically tuning the light–matter interactions. The observed exceptional points do not require any spatial or polarization degrees of freedom and result solely from the transition from weak to strong light–matter coupling. It was demonstrated that they do not coincide with the threshold for photon lasing, confirming previous theoretical predictions [Phys. Rev. Lett. 122, 185301 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.185301, Optica 7, 1015 (2020)OPTIC82334-253610.1364/OPTICA.397378]. Using a technique where a strong coherent laser pump induces up-converted excitations, we encircle the exceptional point in the parameter space of coupling strength and particle momentum. Our method of local optical control of light–matter coupling paves the way to the investigation of fundamental phenomena, including dissipative phase transitions and non-Hermitian topological states.