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We predict that the onset of gluon saturation can be uniquely identified using incoherent J/ψ production in Pb–Pb collisions at currently accessible energies of the LHC. The diffractive incoherent photo-production of a J/ψ vector meson off a hadron provides information on the partonic structure of the hadron. Within the Good-Walker approach it specifically measures the variance over possible target configurations of the hadronic colour field. For this process then, gluon saturation sets in when the cross section reaches a maximum, as a function of the centre-of-mass energy of the photon-hadron system (W), and then decreases. We benchmark the energy-dependent hot-spot model against data from HERA and the LHC and demonstrate a good description of the available data. We show that the study of the energy dependence of the incoherent production of J/ψ allows us to pinpoint the onset of saturation effects by selecting the region of Mandelstam-t around 1 GeV2 where the contribution of hot spots is dominant. We predict the onset of saturation in a Pb target to occur for W around a few hundred GeV. This can be measured with current data in ultra-peripheral Pb–Pb collisions at the LHC.