Although the quantum dynamics of gravity in a Universe with vanishing cosmological constant is of indisputable theoretical interest, a description that is both non-perturbatively complete and computationally tractable is currently lacking. The aim of this talk is to show how a two-dimensional toy model of flat space gravity, introduced by Cangemi and Jackiw in the nineties, partially fills this gap. We argue it is the simplest theory of flat gravity and show how precise bulk computations of quantum observables can be non-perturbatively completed by a random matrix model. (Based on arXiv:2205.02240, 2208.05974 and 2209.14372)