We use a thermal history of the mantle to calculate the evolution of oceanic crustal thickness over Earth history and use residual depth anomalies from the present-day Pacific to find the crustal thickness range (9.2-11.6 km) where the subduction style changes from mainly flat to mainly steep. We find that steep subduction was well developed by 2.5 Ga, which coincides with a major change in sedimentary rare-earth element patterns. Over 50% of all oceanic crust subducted steeply by 2.0-1.6 Ga, the same interval over which the average thickness of continental plates declined rapidly. Because producing thick plates requires many episodes of flat subduction, our model can explain why there are no known thick plates <1.6 Ga.