Solid phase epitaxy is a crystallization technique used to produce high-quality thin films. Lateral solid phase epitaxy furthermore enables the realization of nonplanar structures, which are interesting, e.g., in the field of spintronics. Here, we demonstrate lateral solid phase epitaxy of yttrium iron garnet over an artificial edge, such that the crystallization direction is perpendicular to the initial seed. We use single-crystalline garnet seed substrates partially covered by a SiOx film to study the lateral crystallization over the SiOx mesa. The yttrium iron garnet layer retains the crystal orientation of the substrate not only when in direct contact with the substrate but also across the edge on top of the SiOx mesa. By controlling the crystallization dynamics it is possible to almost completely suppress the formation of polycrystals and to enable epitaxial growth of single-crystalline yttrium iron garnet on top of mesas made from ceramic materials. From a series of annealing experiments, we extract an activation energy of 3.0eV and a velocity prefactor of 6.5×1014nm/s for the lateral epitaxial crystallization along the (100) direction. Our results pave the way to engineer single-crystalline nonplanar yttrium iron garnet structures with controlled crystal orientation.