Global Navigation Satellite Systems (GNSS)-based earthquake early warning (EEW) algorithms estimate fault finiteness and unsaturated moment magnitude for the largest, most damaging earthquakes. Because large events are infrequent, algorithms are not regularly exercised and insufficiently tested on few available data sets. We use 1300 realistic, time-dependent, synthetic earthquakes on the Cascadia megathrust to rigorously test the Geodetic Alarm System. Solutions are reliable once six GNSS stations report static offsets, which we require for a first alert. Median magnitude and length errors are -0.150.24units and -31 40% for the first alert, and -0.040.11units and +731% for the final solution. We perform a coupled test of a seismic-geodetic EEW system using synthetic waveforms for a M(w)8.7 scenario. Seismic point-source solutions result in severely underestimated peak ground acceleration. Geodetic finite-fault solutions provide more accurate predictions at larger distances, thus increasing warning times. Hence, GNSS observations are essential in EEW to accurately characterize large (out-of-network) events and correctly predict ground motion. Plain Language Summary Earthquake early warning algorithms that use ground motion data measured by the Global Navigation Satellite System (GNSS) complement traditional seismic approaches. GNSS instruments, unlike seismometers, reliably record permanent ground movement. These data enable reliable estimation of total fault length and magnitude for the largest earthquakes. As there are not many large earthquakes, the system is not tested regularly. We use computer-simulated earthquake scenarios to test the Geodetic Alarm System, a GNSS-based algorithm developed for the western U.S. The Geodetic Alarm System satisfactorily recovers magnitude and fault length for 1300 synthetic earthquakes. The fault solutions provide more accurate predictions of ground shaking than seismic algorithms. We demonstrate that GNSS observations are essential in earthquake early warning to accurately characterize large events and correctly predict ground shaking.