Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects, or local disorder and can even survive some random deformations of their crystalline structures. However, they always break down when the level of disorder or amorphism gets too large, transitioning to a topologically trivial Anderson insulating phase. We demonstrate a two-dimensional amorphous topological regime that survives arbitrarily strong levels of amorphism. We implement it for electromagnetic waves in a nonreciprocal scattering network and experimentally demonstrate the existence of unidirectional edge transport in the strong amorphous limit. This edge transport is shown to be mediated by an anomalous edge state whose topological origin is evidenced by direct topological invariant measurements. Our findings extend the reach of topological physics to a class of systems in which strong amorphism can induce, enhance, and guarantee the topological edge transport instead of impeding it.