The near-threshold photoproduction of $J/psi$ is regarded as one golden process to unveil the nucleon mass structure, pentaquark state involving the charm quarks, and the poorly constrained gluon distribution of the nucleon at large $x$ ($>0.1$). In this paper, we present an analysis of the current experimental data under a two-gluon exchange model, which shows a good consistency. Using a parameterized function form with three free parameters, we have determined the nucleonic gluon distribution at the $J/psi$ mass scale. Moreover, we predict the differential cross section of the electroproduction of $J/psi$ as a function of the invariant mass of the final hadrons $W$, at EicC, as a practical application of the model and the obtained gluon distribution. According to our estimation, thousands of $J/psi$ events can be detected per year on EicC near the threshold. Therefore, the relevant experimental measurements are suggested to be carried out on EicC.
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