The near-threshold photo or electroproduction of heavy vector quarkonium off the proton is studied in quantum chromodynamics. Similar to the high-energy limit, the production amplitude can be factorized in terms of gluonic generalized parton distributions and the quarkonium distribution amplitude. At the threshold, the threshold kinematics has a large skewness parameter xi, leading to the dominance of the spin2 contribution over higher-spin twist-2 operators. Thus, threshold production data are useful to extract the gluonic gravitational form factors, allowing studying the gluonic contributions to the quantum anomalous energy, mass radius, spin, and mechanical pressure in the proton. We use the recent GlueX data on the J/Psi. photoproduction to illustrate the potential physics impact from the high-precision data from the future Jefferson Laboratory 12 GeV and Electron-Ion Collider physics program.