We investigate the generation of the baryon asymmetry within the framework of cosmological gra­vi­ta­tional particle production, employing the Bogoliubov approach. We examine two well-known baryogenesis scenarios, namely baryogenesis in Grand Unified Theories (GUT) and leptogenesis, while considering reheating temperatures sufficiently low for thermal processes to be negligible. Considering $\alpha-$attractor T-models for the inflaton potential, we demonstrate that GUT baryogenesis from scalar decays can be successful across a large range of conformal couplings with gravity, without necessitating substantial levels of CP violation. In the case of leptogenesis, we find that the reheating temperature should be $T_{\rm RH}\lesssim 10^{6}~{\rm GeV}$ for right-handed neutrino masses $M_1 \lesssim 6 \times 10^{12}~{\rm GeV}$ to generate the observed asymmetry.