We study the young S-stars within a distance of 0.04 pc from the supermassive black hole in the center of our Galaxy. Given how inhospitable the region is for star formation, their presence is more puzzling the younger we estimate their ages. In this study, we analyse the result of 12 years of high resolution spectroscopy within the central arcsecond of the Galactic Center (GC). By co-adding between 55 and 105 hours of spectra we have obtained high signal to noise H- and K-band spectra of eight stars orbiting the central supermassive black hole. Using deep H-band spectra, we show that these stars must be high surface gravity (dwarf) stars. We compare these deep spectra to detailed model atmospheres and stellar evolution models to infer the stellar parameters. Our analysis reveals an effective temperature of 21000-28500 K, a rotational velocity of 60-170 km/s, and a surface gravity of 4.1-4.2. These parameters imply a spectral type of B0-B3V for these stars. The inferred masses lie within 8-14 Msun. We derive an age of 6.6^{+3.4}{-4.7} Myr for the star S2, which is compatible with the age of the clockwise rotating young stellar disk in the GC. We estimate the age of all other studied S-stars to be less than 15 Myr, which are compatible with the age of S2 within the uncertainties. The relatively low ages for these S-stars favor a scenario in which the stars formed in a local disk rather than the field-binary-disruption scenario throughout a longer period of time.