Continents are unique to Earth and played a role in coevolution of the atmosphere, hydrosphere, and biosphere. Debate exists, however, regarding continent formation and the onset of subduction-driven plate tectonics. We present Ca isotope and trace-element data from modern and ancient (4.0 to 2.8 Ga) granitoids and phase equilibrium models indicating that Ca isotope fractionations are dominantly controlled by geothermal gradients. The results require gradients of 500-750 °C/GPa, as found in modern (hot) subduction-zones and consistent with the operation of subduction throughout the Archaean. Two granitoids from the Nuvvuagittuq Supracrustal Belt, Canada, however, cannot be explained through magmatic processes. Their isotopic signatures were likely inherited from carbonate sediments. These samples (> 3.8 Ga) predate the oldest known carbonates preserved in the rock record and confirm that carbonate precipitation in Eoarchaean oceans provided an important sink for atmospheric CO2. Our results suggest that subduction-driven plate tectonic processes started prior to ~3.8 Ga.