In the present work, the identification of two hexagonal phases of germanium oxides (namely GeO₂ and GeO) through the vibrational and optical properties is reported using density functional theory calculations. While structural optimizations show that single-layer GeO₂ and GeO crystallize in 1T and buckled phases, phonon band dispersions reveal the dynamical stability of each structure. First-order off-resonant Raman spectral predictions demonstrate that each free-standing single-layer possesses characteristic peaks that are representative for the identification of the germanium oxide phase. On the other hand, electronic band dispersion analysis shows the insulating and large-gap semiconducting nature of single-layer GeO₂ and GeO, respectively. Moreover, optical absorption, reflectance, and transmittance spectra obtained by means of G₀W₀-BSE calculations reveal the existence of tightly bound excitons in each phase, displaying strong optical absorption. Furthermore, the excitonic gaps are found to be at deep UV and visible portions of the spectrum, for GeO₂ and GeO crystals, with energies of 6.24 and 3.10 eV, respectively. In addition, at the prominent excitonic resonances, single-layers display high reflectivity with a zero transmittance, which is another indication of the strong light–matter interaction inside the crystal medium.