The major challenge in the development of earthquake early warning (EEW) systems is the achievement of a robust performance at largest possible warning time. We have developed a new method for EEW—called PreSEIS (Pre-SEISmic)—that is as quick as methods that are based on single station observations and, at the same time, shows a higher robustness than most other approaches. At regular timesteps after the triggering of the first EEW sensor, PreSEIS estimates the most likely source parameters of an earthquake using the available information on ground motions at different sensors in a seismic network. The approach is based on two-layer feed-forward neural networks to estimate the earthquake hypocenter location, its moment magnitude, and the expansion of the evolving seismic rupture. When applied to the Istanbul Earthquake Rapid Response and Early Warning System (IERREWS), PreSEIS estimates the moment magnitudes of 280 simulated finite faults scenarios (4.5≤M≤7.5) with errors of less than ±0.8 units after 0.5 sec, ±0.5 units after 7.5 sec, and ±0.3 units after 15.0 sec. In the same time intervals, the mean location errors can be reduced from 10 km over 6 km to less than 5 km, respectively. Our analyses show that the uncertainties of the estimated parameters (and thus of the warnings) decrease with time. This reveals a trade-off between the reliability of the warning on the one hand, and the remaining warning time on the other hand. Moreover, the ongoing update of predictions with time allows PreSEIS to handle complex ruptures, in which the largest fault slips do not occur close to the point of rupture initiation. The estimated expansions of the seismic ruptures lead to a clear enhancement of alert maps, which visualize the level and distribution of likely ground shaking in the affected region seconds before seismic waves will arrive.