Creating true muonium via charmonium radiative decay

True muonium, the bound state of a muon and an antimuon ($\mu^+\mu^-$), has long been theoretically predicted but remains experimentally elusive. We investigate the production of true para-muonium in the radiative decay of $J/\psi$ meson,and analyze the prospects for detecting true muonium in current and future high-energy $e^+e^-$ experiments, particularly focusing on the BESIII experiment and the proposed Super Tau-Charm Facility. Although the events are rare at the super tau-charm facility, the detection of true para-muonium via $J/\psi$ radiative decays could become feasible at its future updates.