What about Hydrogen ?
Oxygen is a relatively common element on Mars, at least when compared to hydrogen:
The red planet is red primarily because of iron oxide (rust), so heat the soil hot enough and Oxygen, and other gases, will be released.
Oxygen can as has been done with MOXIE extracted from carbon dioxide in the thin Martian atmosphere.
Oxygen can also be extracted through electrolysis from water that is found in deposits of ice mostly at the frigid poles (−153 °C; 120 K; −243 °F).
Plants could also create Oxygen from carbon dioxide with enough sunlight. But more than about 0.2% and less than 0.025% carbon dioxide will kill most plants.
Even though the atmosphere on Mars has a pressure *155 times lower than is found on Earth, all the elements found in it: carbon dioxide (95%), molecular nitrogen (2.8%), and argon (2%) could, with enough energy, be used to synthesise an earth like air (78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide). Looking at the elements present in the Martian atmosphere a simpler atmosphere to synthesise for humans to live in might be 46.09% nitrogen, 20.95% oxygen, 32.92% argon, 0.04% carbon dioxide, but that would probably not be as useful for nitrogen-fixing bacteria for plants as 78.08% nitrogen.
To create water or rocket fuel one element you need is hydrogen.
About ~0.6% of mars regolith (soil) by weight is (water soluble) Perchlorate, and of that roughly 20% is ammonium perchlorate (NH4ClO4) which contains hydrogen. I would be very interested in the process that NASA plan to use to purify and extract Hydrogen from about 0.12% ammonium perchlorate found in the soil of mars to synthesise drinking water and rocket fuel. One problem with processing regolith would be that it requires more energy (collection and transportation) typically than processing the Martian atmosphere.
Another option would be to extract water from the thin Martian atmosphere, where tiny trace amounts (~0.03%) can be found, the simplest way would be to condense it as ice by cooling the Martian atmosphere entering and leaving through a recuperator to minimise the energy used.
* Mars atmospheric pressure (ground level) 652 Pascal 0.00643 atm 0.0945 psi 0.006518 bar
* Earth atmospheric pressure (sea level) 101353 Pascal 1.00000 atm 14.7 psi 1.01353 bar
I suspect that multiple synthesised atmospheres initially could be very useful, one optimised for plants to generate maximise biomass (more N2 and more CO2) and a separate atmosphere with less CO2 and more argon (to increase the nitrogen available for plants) for humans. Both would still be safe for humans to breath.