This file contains all the data, as well as the code necessary to reproduce the results of Jae-Mo Lihm and Samuel Ponce, "Non-perturbative self-consistent electron-phonon spectral functions and transport." Electron-phonon coupling often dominates the electron spectral functions and transport properties. However, studies of this effect in real materials have largely relied on perturbative one-shot methods due to the lack of a first-principles theoretical and computational framework. Here, we present a self-consistent theory and implementation for the non-perturbative calculations of spectral functions and conductivity due to electron-phonon coupling. Applying this method to monolayer InSe, we demonstrate that self-consistency qualitatively affects the spectral function and transport properties compared to state-of-the-art one-shot calculations and allow one to reconcile experimental angle-resolved photoemission experiments. The developed method can be widely applied to materials with dominant electron-phonon coupling at moderate computational cost.