We report the total and differential cross sections for J/ψ photoproduction with the large acceptance GlueX spectrometer for photon beam energies from the threshold at 8.2 GeV up to 11.44 GeV and over the full kinematic range of momentum transfer squared, t. Such coverage facilitates the extrapolation of the differential cross sections to the forward (t=0) point beyond the physical region. The forward cross section is used by many theoretical models and plays an important role in understanding J/ψ photoproduction and its relation to the J/ψ-proton interaction. These measurements of J/ψ photoproduction near threshold are also crucial inputs to theoretical models that are used to study important aspects of the gluon structure of the proton, such as the gluon generalized parton distribution of the proton, the mass radius of the proton, and the trace anomaly contribution to the proton mass. We observe possible structures in the total cross section energy dependence and find evidence for contributions beyond gluon exchange in the differential cross section close to threshold, both of which are consistent with contributions from open-charm intermediate states.