Dr. G. Arnold is one of the world's leading authorities in molybdenum redox, which is a cornerstone of the anoxic (oxygen deficient) early-atmosphere model.
You can read many paper by her-and-team that reinforce the anoxic atmosphere hypothesis.
A simple way to think of the evidence: Molybdenum is very sensitive to redox, an chemical process that involves oxygen. These charts on p1904 show that no redox occurred below a certain depth that is correlated with time... i.e. when that rock was exposed to the earth's surface or ocean floor. Since no redox occurred below a certain level, no oxygen was in the atmosphere.
Whether or not anoxic atmospheres are pre/non-biotic...... that is a whole separate discussion. (and why Science is so hard for many to care about, I think. People want simple narrative packages, without many loose ends)