Plate tectonics is a fundamental factor in the sustained habitability of Earth, but its time of onset is unknown, with ages ranging from the Hadaean to Proterozoic eons1–3. Plate motion is a key diagnostic to distinguish between plate and stagnant-lid tectonics, but palaeomagnetic tests have been thwarted because the planet’s oldest extant rocks have been metamorphosed and/or deformed4. Herein, we report palaeointensity data from Hadaean-age to Mesoarchaean-age single detrital zircons bearing primary magnetite inclusions from the Barberton Greenstone Belt of South Africa5. These reveal a pattern of palaeointensities from the Eoarchaean (about 3.9 billion years ago (Ga)) to Mesoarchaean (about 3.3 Ga) eras that is nearly identical to that defined by primary magnetizations from the Jack Hills (JH; Western Australia)6,7, further demonstrating the recording fidelity of select detrital zircons. Moreover, palaeofield values are nearly constant between about 3.9 Ga and about 3.4 Ga. This indicates unvarying latitudes, an observation distinct from plate tectonics of the past 600 million years (Myr) but predicted by stagnant-lid convection. If life originated by the Eoarchaean8, and persisted to the occurrence of stromatolites half a billion years later9, it did so when Earth was in a stagnant-lid regime, without plate-tectonics-driven geochemical cycling.