My answer goes a little beyond the evidence -- there isn't much evidence.
There's a lot of free oxygen now. This oxygen did not suddenly come from underground or from space. So it used to be attached to something. The question is, what was it attached to, and what happened to what it was attached to?
First off, there's every reason to think that bacteria already did oxidative phosporylation before there was any free oxygen. It does not require free oxygen, it requires an electron acceptor. O2 provides the most energy, but many other reactants provide some energy, and the bacterial kingdom uses a bewildering variety of them. To use a different electron acceptor requires only one different enzyme -- the rest of the pathway can be the same.
So before there was free oxygen, prokaryotes did arbitrage -- they evolved to use the best electron donor/electron acceptor pair they could find under whatever conditions they faced at the moment. And everything they used for that had to be created in a cycle. Anything which they used up that was not replaced, would quickly be gone.
Before there was free oxygen, photosynthesis still got done. Some bacteria used H2S as an electron donor, creating S which could later be reduced for energy. Some created H2. Some could reduce CO2 so that they could use the carbon and oxygen to make structures they needed. Some could not, but could still get energy from light. One way to do that was almost the same as oxidative phosphorylation, it used the absorbed light energy for electron transport instead of using redox energy, in practically the same pathway.
Cycles. Every reaction must be undone, or its products will increase to the point that the reaction gets very slow. The exception is products that change state. A solid or gas product won't inhibit the reaction much.
So, a bewildering variety of electron donors and acceptors. Photosynthesis creates energetic pairs of molecules or ions. Then redox creates less-energetic pairs of molecules or ions.
What was it that was bound to oxygen in the old days, that was not bound later?
Hydrogen. One form of photosynthesis creates H2. Maybe, at some times a whole lot of H2 was created which was lost to space. Just as much O and less H leaves room for O2 left over.
Sulfur. Maybe most of the sulfur in the oceans was stored as SO3.
H2 SO3 -> S + H2O + O2.
Sulfur can be oxidized -- SO3. Or it can replace Oxygen as an oxidizer -- H2O -> H2S etc.
So by changing states it could affect free O2. And solid sulfur could wind up on the ocean bottom where it would be subducted.
- Heavy metals + sulfur. Maybe there was a lot of iron and nickel etc dissolved in the ancient ocean, along with a lot of sulfur. Iron sulfate is fairly soluble at room temperature, nearly 300 grams/liter. Provided it is not alkaline. But iron sulfide is not soluble. Lots of other heavy metals behave similarly.
F3O4 + 4 H2SO3 -> F3S4 + 6 O2 + 4 H20 (and many other combinations)
- Nitrogen. Nitrogen can be reduced to NH4 or oxidized to NO2 or NO3.
2 NO2 + 4 H+ = N2 + O2 + 2 H2O
Perhaps there was a time when the atmosphere had only 75% as much N2 as it does now, and no O2. This reaction would imply the oceans used to be more acidic than they are now. But there could be other reactions that would counteract that, and there were lots of other buffers.
- Silicon. Silicon is usually oxidized, SiO2. It doesn’t have to have that ratio. Other silicon compounds are possible, eg carborundum SiC, and perryite Fe5Si2 which is stable in acid water, silicon nitride Si3N4, silicon phosphide SiP2 etc . Siloxanes can have ratio Si:O of 1:1. Low molecular weight siloxanes are produced by modern anaerobic biogas fermenters, though it could possibly be eukaryotes producing them. There is potentially a tremendous amount of SiO2 available to release oxygen, although only a little of it is soluble at any one time.
Or bacteria could have metabolized silicic acid into insoluble compounds that had less oxygen. This is entirely hypothetical since only a little carborundum has been discovered, and the rest would have had to be subducted.
Banded iron formations do though have layers of amorphous quartz. Silicon dioxide was being removed from the water. Perhaps it was alternately iron being removed while soluble siloxanes accumulated in water, and then the siloxanes were converted to silica and removed while iron accumulated in water.
It was a complicated web of reactions. Photosynthesis provided the energy to create energy-rich chemicals. Meanwhile every organism that was not photosynthetic was busy finding its best mix of catalyzing chemical reactions that provided energy, versus creating the molecules needed to grow and reproduce. Strange things happened.