Question: How is hydrogen produced when there is no atmospheric oxygen?
Sentence: In the absence of atmospheric oxygen (O_2), in deep geological conditions prevailing far away from Earth atmosphere, hydrogen (H_2) is produced during the process of serpentinization by the anaerobic oxidation by the water protons (H+) of the ferrous (Fe2+) silicate present in the crystal lattice of the fayalite (Fe_2SiO_4, the olivine iron-endmember).
Answer in sentence: yes