Cosmic rays (CRs) with energies below $10^{18}$ electron volts (eV) are believed to be atomic nuclei originating from within our Galaxy, while there is a transition to extragalactic cosmic rays occurring around $10^{18}$ eV. The characterization of this transition is important for understanding new physics phenomena proposed for Ultra-High Energy Cosmic Rays (UHECRs) with center-of-mass energies above 50 TeV. In this study, we conducted air-shower simulations using CORSIKA to investigate the energy range from just below the ankle ($10^{17}$ eV) up to the highest energies ($10^{20}$ eV), and compared our results with observations of the energy spectrum and composition obtained from the Auger experiment. To determine the flux and elemental ratios just below the ankle, we utilized data on the abundances and flux of low-energy cosmic ray components obtained from the KASCADE experiment. Due to confinement arguments, heavier nuclei exhibit greater bending in a given galactic magnetic field, allowing them to reach higher energies. To account for this, we incorporated an exponential suppression term in the flux of heavier nuclei, which depends on their atomic number. Regarding extragalactic cosmic rays, we assumed a composition dominated by lighter elements; however, we also considered the presence of "new physics" effects at energies above 50 TeV, as discussed in our previous work Romanopoulos, Pavlidou, and Tomaras (2022). Our analysis demonstrates that the observed penetration depth ($X_\text{max}$) and its standard deviation ($\sigma_{X_\text{max}}$) align well with our assumption of a Galactic CR composition. Additionally, we found that the proposed new physics at a center-of-mass energy of 140 TeV requires a cross-section in the range of 752-836 mb and a multiplicity factor 1.7-3.6 times higher than predicted by the standard model. Furthermore, we conducted an investigation into the muon production within the same framework of our study. Our analysis reveals that the muon production in showers is still in disagreement with observations for energies below the ankle.