The Origins Space Telescope (Origins) will have a 5.9-m diameter primary mirror cooled to 4.5 K and will be equipped with three instruments, two of which will cover the far-IR (λ  =  25 to 588  μm). These far-IR instruments will require large arrays (∼10⁴ detectors) of ultrasensitive detectors, with noise equivalent powers (NEPs) as low as 3  ×  10^−  20  W Hz^−  1/2. Kinetic inductance detectors (KIDs) have already demonstrated the array format, modularity, and readout multiplexing density requirements for Origins; the only aspect that requires improvement is the per-pixel sensitivity. We show how KIDs can meet the sensitivity target, focusing on two existing architectures that together demonstrate the key necessary attributes. Arrays of antenna-coupled coplanar waveguide resonators have achieved NEPs of 3  ×  10^−  19  W Hz^−  1/2 in laboratory demonstrations at 350  μm; they demonstrate excellent material properties as well as array-level integration and performance. Lumped element detectors such as those under development for balloon-borne spectroscopy at 10 to 350  μm demonstrate flexibility in coupling to shorter-wavelengths, reducing active volume, and providing a means for suppressing capacitor noise. A straightforward combination of the elements of these already-demonstrated devices points to a low-volume design that is expected to meet the Origins sensitivity targets.