Linear absorption spectroscopy has been the work-horse experimental method for probing hydrated electrons for the last several decades. There has been essentially no work, however, characterizing the non-linear spectroscopy, such as the 2-dimensional electronic spectrum (2DES), of this species, despite the wealth of additional information that the 2DES provides. Nonlinear spectroscopy can directly measure homogeneous and inhomogeneous line-widths, quantify spectral diffusion, and probe the characteristic solvent dynamics that drive temporal line-shape evolution. This is particularly attractive for studying different simulation models of the hydrated electron. Most such models produce a roughly spherical charge density that predict a linear absorption spectrum in reasonable agreement with experiment, even though the solvent structure and dynamical fluctuations underlying these models are quite different. Thus, the temporal evolution of the 2DES signal provides an experimentally verifiable means to discriminate between different models and levels of theory for this species. In this work, we present the first theoretical predictions of the hydrated electron's 2DES spectrum. We show that two different one-electron models that produce very similar linear absorption spectra display distinct temporal dynamics of their 2DES signals. The results function not only as a prediction that can be compared directly to future experiments, but illustrate the utility of nonlinear spectroscopy in understanding the solvation dynamics of fully solvent-supported hydrated electron systems.