  We investigate the realization of the emergent universe scenario in theories
with natural UV cutoffs, namely a minimum length and a maximum momentum,
quantified by a new deformation parameter in the generalized uncertainty
principle. We extract the Einstein static universe solutions and we examine
their stability through a phase-space analysis. As we show, the role of the new
deformation parameter is crucial in a twofold way: Firstly, it leads to the
appearance of new Einstein static universe critical points, that are absent in
standard cosmology. Secondly, it provides a way for a graceful exit from the
Einstein static universe into the expanding thermal history, that is needed for
a complete and successful realization of the emergent universe scenario.
