Abstract Motivated by the recent experiment (Vaidya et al 2020 Science 368 160) on spin pumping from sub-THz radiation-driven uniaxial antiferromagnetic insulator (AFI) MnF₂ into heavy metal (HM) Pt hosting strong spin-orbit (SO) coupling, we compute and compare pumped spin currents in Cu/MnF₂/Cu and Pt/MnF₂/Cu heterostructures. Recent theories of spin pumping by AFI have relied on simplistic Hamiltonians (such as tight-binding) and the scattering approach to quantum transport yielding the so-called interfacial spin mixing conductance (SMC), but the concept of SMC ceases to be applicable when SO coupling is present directly at the interface. In contrast, we use a more general first-principles quantum transport approach which combines noncollinear density functional theory with Floquet-nonequilibrium Green’s functions in order to take into account: SO-proximitized AFI as a new type of quantum material, different from isolated AFI and brought about by AFI hybridization with adjacent HM layer; strong SO coupling at the interface; and evanescent wavefunctions penetrating from Pt or Cu into AFI layer to make its interfacial region conducting rather than insulating as in the isolated AFI. The DC component of pumped spin current I D C S z vs. precession cone angle θ l of the Néel vector l of AFI does not follow putative I DC S z ∝ sin 2 θ l , except for very small angles θ l ≲ 10 ° for which we define an effective SMC from the prefactor and find that it doubles from MnF₂/Cu to MnF₂/Pt interface. In addition, the angular dependence I D C S z ( θ l ) differs for opposite directions of precession of the Néel vector, leading to twice as large SMC for the right-handed than for the left-handed chirality of the precession mode.