  Recent pulsar timing array (PTA) experiments have reported strong evidence of
the stochastic gravitational wave background (SGWB). If interpreted as
primordial gravitational waves (GWs), the signal favors a strongly blue-tilted
spectrum. Consequently, the nonsingular cosmology, which is able to predict a
strongly blue-tilted GW spectrum with $n_T \simeq 2$ on certain scales, offers
a potential explanation for the observed SGWB signal. In this paper, we present
a Genesis-inflation model capable of explaining the SGWB signal observed by the
PTA collaborations while also overcoming the initial singularity problem
associated with the inflationary cosmology. Furthermore, our model predicts
distinctive features in the SGWB spectrum, which might be examined by
forthcoming space-based gravitational wave experiments.
