We irradiated binary ice mixtures of ammonia (NH3) and oxygen (O-2) ices at astrophysically relevant temperatures of 5.5 K with energetic electrons to mimic the energy transfer process that occurs in the track of galactic cosmic rays. By monitoring the newly formed molecules online and in situ utilizing Fourier transform infrared spectroscopy complemented by temperature-programmed desorption studies with single-photon photoionization reflectron time-of-flight mass spectrometry, the synthesis of hydroxylamine (NH2OH), water (H2O), hydrogen peroxide (H2O2), nitrosyl hydride (HNO), and a series of nitrogen oxides (NO, N2O, NO2, N2O2, N2O3) was evident. The synthetic pathway of the newly formed species, along with their rate constants, is discussed exploiting the kinetic fitting of the coupled differential equations representing the decomposition steps in the irradiated ice mixtures. Our studies suggest the hydroxylamine is likely formed through an insertion mechanism of suprathermal oxygen into the nitrogen-hydrogen bond of ammonia at such low temperatures. An isotope-labeled experiment examining the electron-irradiated D3-ammonia-oxygen (ND3-O-2) ices was also conducted, which confirmed our findings. This study provides clear, concise evidence of the formation of hydroxylamine by irradiation of interstellar analogue ices and can help explain the question how potential precursors to complex biorelevant molecules may form in the interstellar medium.