Cerebral hypoxia is a severe injury caused by oxygen deprivation to the brain. Hypoxia in the neonatal period increases the risk for the development of neurological disorders, including hypoxic-ischemic encephalopathy, cerebral palsy, periventricular leukomalacia, and hydrocephalus. It is crucial to recognize hypoxia as soon as possible because early intervention improves outcomes. Photoacoustic imaging, using at least two wavelengths, through a spectroscopic analysis, can measure brain oxygen saturation. Due to the spectral coloring effect arising from the dependency of optical properties of biological tissues to the wavelength of light, choosing the right wavelength-pair for efficient and most accurate oxygen saturation measurement and consequently quantifying hypoxia at a specific depth is critical. Using a realistic neonate head model and Monte Carlo simulations, we found practical wavelength-pairs that quantified regions with hypoxia most accurately at different depths down to 22 mm into the cortex neighboring the lateral ventricle. We also demonstrated, for the first time, that the accuracy of the sO2 measurement can be increased by adjusting the level of light energy for each wavelength-pair. Considering the growing interest in photoacoustic imaging of the brain, this work will assist in a more accurate use of photoacoustic spectroscopy and help in the clinical translation of this promising imaging modality. Please note that explaining the effect of acoustic aberration of the skull is not in the scope of this study.