  The emergent mechanism provides a possible way to resolve the big bang
singularity problem by assuming that our universe originates from the Einstein
static (ES) state. Thus, the existence of a stable ES solution becomes a very
crucial prerequisite for the emergent scenario. In this paper, we study the
stability of an ES universe in gravity theory with a non-minimal coupling
between the kinetic term of a scalar field and the Einstein tensor. We find
that the ES solution is stable under both scalar and tensor perturbations when
the model parameters satisfy certain conditions, which indicates that the big
bang singularity can be avoided successfully by the emergent mechanism in the
non-minimally kinetic coupled gravity.
