This oxygen was produced by the photodissociation of water vapor and the loss of light hydrogen to space.
"Microbial mats, which fossilize into stromatolites, have been abundant on Earth for at least 3.5 billion years, and yet for the first billion years of their existence, there was no oxygen for photosynthesis."
That's not true.
The fossil record of cyanobacteria now goes back to over four billion years.
Lots of things are possible but one thing is certain. Some UV radiation protection for life to begin on Earth (or elsewhere) was needed at the surface.
Although there is widespread speculation on the geological setting for the origin of life, the earliest geological and biological evidence for early life and the putative conditions on the early Archean or Hadean Earth provide some environmental constraints. Several theories suggest a hot, aqueous environment for the origin of life (e.g., Pace, 1991; Stetter, 2005), and submarine hydrothermal vents have been widely proposed as candidate environments for prebiotic chemistry (e.g., Orgel, 1998; Nisbet and Sleep, 2001; Copley et al.,2007; Martin et al.,2008; Russell et al.,2013). Indeed, while still debated, many phylogenetic tree reconstructions when using molecular analyses of 16S rRNA combined with metabolic studies suggest a hyperthermophilic last universal common ancestor (LUCA) (Woese et al.,1990; Pace, 1991; Di Giulio, 2001, 2003, 2007; Schwartzman and Lineweaver, 2004; Brack et al.,2010).
It is even possible that the evolution of photosynthesis supplied the required O2 to maintain an ozone layer, and limit the loss of earth's water.
This visualization of Simulation 28 shows surface air temperature (Celsius) 2.9 billion years ago for a hypothetical Venus having a nitrogen (N2)-dominated atmosphere with .25-bar surface pressure and an Earth topography with a 310-meter deep ocean. It was the most Earth-like of the 45 simulations, even allowing for the possibility of snow at higher elevations. Figure from M.J. Way and A.D. Del Genio, J. Geophys. Res. Planets.
It was recently proposed that Archean, spherical, iron-rich (type I) micrometeorites could have been oxidized by modern levels of O2 in the upper atmosphere (10, 11). However, very low levels of O2 in the Archean atmosphere inferred from a large variety of proxies [e.g., (12)] motivate considering oxidation by CO2 as an alternative (13). Thus, the micrometeorites could provide a new constraint on Archean CO2 levels.
With a mean surface pressure of 0.23 ± 0.23 bar, our model predicts a CO2 partial pressure of >0.16 ± 0.16 bar (2σ). Provided some methane was present, such as 0.5% (30), this thin, CO2-rich atmosphere could provide enough greenhouse warming to sustain liquid water under a faint young Sun [e.g., (31)]. Atmospheric methane would warm the surface during the Archean as a greenhouse gas but is not expected to interact with molten, Fe-rich micrometeorites (10) and thus should not alter their oxidation state.
"This is a biochemist inspired minority idea which is problematic due to all converging evidence for submarine hydrothermal vents.""Lots of things are possible but one thing is certain. Some UV radiation protection for life to begin on Earth (or elsewhere) was needed at the surface."
The UV damaging radiation from the Sun cannot be minimized or passed off with ad hoc special pleading.