The study explored the possibility of constructing cosmological models of inflation without initial singularity. The main focus was on the model of a closed universe, which has a constant radius in the asymptotic past and undergoes inflation in the future, leading to a universe dominated by a massless scalar field ('kination'). This evolution is an analog of the Genesis model with an inflationary exit but in a closed universe. The key feature of the examined model is the absence of the Null Energy Condition (NEC), allowing the use of the simplest quadratic subclass of the Horndeski theory. This subclass essentially represents a scalar field with an unusual kinetic term and General Relativity. By employing the Horndeski theory framework for a closed Universe, it was demonstrated that the model remains stable at all times, meaning there are no ghosts or gradient instabilities. Furthermore, the spectrum of scalar perturbations was numerically determined, which is crucial as it corresponds to observable data.