Within the theoretical framework of the generalized factorization of perturbative QCD, i.e., the higher-twist expansion formalism, we perform the first global analysis of the jet transport coefficient ($\hat q$) in cold nuclear matter, in which analysis we take into account the available data on various types of transverse momentum broadening in $e$A and $p$A collisions, as well as the nuclear modification of the structure functions in DIS. The global analysis suggests a universal and kinematics-dependent $\hat q=\hat q\,(x,Q^2)$ in cold nuclear matter, which would be instructive for understanding the jet quenching phenomena and the property of quark-gluon plasma in a more accurate way. Further more, utilizing the Hessian matrix, we evaluate the uncertainty of the extracted $\hat q\,(x,Q^2)$ under the constraints of the current data and generate the error evaluation sets of $\hat q\,(x,Q^2)$, with which we make preliminary predictions for the future EIC experiments at three facilities covering a wide kinematic range.