High-energy photons from blazars can initiate electromagnetic pair cascades interacting with the extragalactic photon background. The charged component of such cascades is deflected and delayed by extragalactic magnetic fields (EGMFs), thereby reducing the observed point-like flux and potentially leading to multi-degree images in the GeV energy range. We calculate the fluence of 1ES 0229+200 as seen by Fermi-LAT for different EGMF profiles using a Monte Carlo simulation for the cascade development. The non-observation of 1ES 0229+200 by Fermi-LAT suggests that the EGMF fills at least 60% of space with fields stronger than G for lifetimes of TeV activity of yr. Thus, the (non-)observation of GeV extensions around TeV blazars probes the EGMF in voids and puts strong constraints on the origin of EGMFs: either EGMFs were generated in a space filling manner (e.g., primordially) or EGMFs produced locally (e.g., by galaxies) have to be efficiently transported to fill a significant volume fraction as, e.g., by galactic outflows.