Our current understanding of the Universe is established through the pristine measurements of structure in the cosmic microwave background (CMB) and the distribution and shapes of galaxies tracing the large scale structure (LSS) of the Universe. One key ingredient that underlies cosmological observables is that the field that sources the observed structure is assumed to be initially Gaussian with high precision. Nevertheless, a minimal deviation from Gaussianity is perhaps the most robust theoretical prediction of models that explain the observed Universe; it is necessarily present even in the simplest scenarios. In addition, most inflationary models produce far higher levels of non-Gaussianity. Since non-Gaussianity directly probes the dynamics in the early Universe, a detection would present a monumental discovery in cosmology, providing clues about physics at energy scales as high as the GUT scale. This white paper aims to motivate a continued search to obtain evidence for deviations from Gaussianity in the primordial Universe. Since the previous decadal, important advances have been made, both theoretically and observationally, which have further established the importance of deviations from Gaussianity in cosmology. Foremost, primordial non-Gaussianities are now very tightly constrained by the CMB. Second, models motivated by stringy physics suggest detectable signatures of primordial non-Gaussianities with a unique shape which has not been considered in previous searches. Third, improving constraints using LSS requires a better understanding how to disentangle non-Gaussianities sourced at late times from those sourced by the physics in the early Universe. The development of the Effective Field Theory of Large Scale Structure and a number of proposed methods to ‘reconstruct’ the initial conditions have contributed significantly to that effort. Lastly, a new technique that utilizes multiple tracers to cancel sample variance in the biased power spectrum, promises constraints on local non-Gaussianities beyond those achievable with higher n-point functions in both the CMB and LSS within the coming decade.
