Past plate motions display a range of variability, including speedups and slowdowns that cannot easily be attributed to changes in mantle related driving forces. One key controlling factor for these variations is the surface topography at convergent margins, as previous modeling shows that the topographic load of large mountain belts consumes a significant amount of the driving forces available for plate tectonics by increasing frictional forces between downgoing and overriding plates. Here we use this insight to pose a new tectonic inverse problem and to infer the growth of mountain belts from a record of past plate convergence. We introduce the automatic differentiation method, which is a technique to produce derivative code free of truncation error by source transformation of the forward model. We apply the method to a publicly available global tectonic thin-shell model and generate a simple derivative code to relate Nazca/South America plate convergence to gross topography of the Andes mountain belt. We test the code in a search algorithm to infer an optimal paleotopography of the Andes 3.2 m.y. ago from the well-known history of Nazca/South America plate convergence. Our modeling results are in excellent agreement with published estimates of Andean paleotopography and support the notion of strong feedback between mountain belt growth and plate convergence.