I will argue that standard Effective Field Theory techniques are inapplicable to describe the very early universe, and that we hence need to turn to a non-perturbative approach. The BFSS (Banks, Fischler, Shenker and Susskind) matrix model is a proposed non-perturbative definition of superstring theory. It is a quantum mechanical model of nine N x N Hermitean matrices (no background space). Recent work has shown that in the large N limit, a continuous space with three large and six small dimensions emerges. We show that thermal fluctuations in a high temperature state of this model yield scale-invariant spectra of cosmological perturbations and gravitational waves. Thus, the BFSS matrix model may yield both emergent space-time and an emergent early universe phase.