For more than half of the time since the earth has been in existence, there was no oxygen. Many bacteria survived without oxygen. However that isn't my concern. I'm concerned with how this was determined. Can someone help me out?
Completely out of my area of expertise so this is a wild guess, butt I'd imagine that down through the layers of rock in which fossils are found, they reached a point where there was no evidence of oxidation to certain metals and minerals???
According to what I have studied in Petroleum Geology concerning organic matter production and preservation, in some areas on the continent, anoxic environment is created. Anoxic environment simply refers to a specific portion of the earth where there is no oxygen. For anoxic environs to be created, there must be; absence of oxygen, low temperature, and absence of light.
Again, there is very small amount of oxygen content in the continental crust than the oceanic crust. In all cases, for these two environments, organisms found here use these small oxygen content later die out of asphyxiation. Like in the sea, light intensity decreases as you move downwards. Sake of this, dark medium is created and this does not favor the existence of oxygen.
In addition to the useful comments above, I guess you can link it back to extremophiles phylogenetics. That will give substantial support to how basic "organism" strive in that environment, and thus, validate that theory of earth without oxygen is logical.