The first measurement of ${}_{\Lambda }{}^{3}H$ and ${}_{\bar{\Lambda }}{}^3\bar{H}$ differential production with respect to transverse momentum and centrality in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is presented. The ${}_{\Lambda }{}^{3}H$ has been reconstructed via its two-charged-body decay channel, i.e., ${}_{\Lambda }{}^{3}H\to {}^3\mathrm{He}+{\pi }^{-}$. A Blast-Wave model fit of the $p_T$-differential spectra of all nuclear species measured by the ALICE collaboration suggests that the ${}_{\Lambda }{}^{3}H$ kinetic freeze-out surface is consistent with that of other nuclei. The ratio between the integrated yields of ${}_{\Lambda }{}^{3}H$ and ${}^3\mathrm{He}$ is compared to predictions from the statistical hadronisation model and the coalescence model, with the latter being favoured by the presented measurements.