The formalism of short-distance factorization, conveyed through the pseudo-distribution approach, connects space-like and light-cone correlators and thus allows for the extraction in lattice QCD of a number of parton distributions. We compute the $t$-dependent parton distribution function of valence quarks in a $\eta_{c}$-meson. After reviewing the main ideas behind the pseudo-distribution formalism, and relying on the analytic structure of Ioffe-time distributions, we come up with a proposal for a model-independent extraction of $t$-dependent parton distribution functions. We present results for the $\eta_{c}$-meson Ioffe time valence $t$-dependent parton distribution function at a renormalization scale of $3~\textrm{GeV}$.