Lattice-resolved, video-rate environmental transmission electron microscopy shows the formation of a liquid Au-Ge layer on sub-30-nm Au catalyst crystals and the transition of this two-phase Au-Ge/Au coexistence to a completely liquid Au-Ge droplet during isothermal digermane exposure at temperatures far below the bulk Au-Ge eutectic temperature. Upon Ge crystal nucleation and subsequent Ge nanowire growth, the catalyst either recrystallizes or remains liquid, apparently stabilized by the Ge supersaturation. We argue that there is a large energy barrier to nucleate diamond-cubic Ge, but not to nucleate the Au-Ge liquid. As a result, the system follows the more kinetically accessible path, forming a liquid even at 240 degrees C, although there is no liquid along the most thermodynamically favorable path below 360 degrees C.