  In order to bypass the big bang singularity, we develop an emergent universe
scenario within a covariant extension of General Relativity known as
\emph{"Energy-Momentum Squared Gravity"}. The extra terms of the model emerge
in the high energy regime. Considering dynamics in a
Friedmann-Lema\^itre-Robertson-Walker background, critical points, representing
stable Einstein static states of the phase space, result as solutions. It then
turns out that as the equation of state parameter $\omega$ gradually declines
from a constant value as $t\rightarrow-\infty$, eventually some of the static
past eternal solutions find the chance to naturally enter into thermal history
through a graceful exit mechanism. In this way, the successful realization of
the emergent universe allows an expanding thermal history without the big bang
singularity for the spatially flat universe free of cosmological constant.
