Is there any evidence telling us what the oxidation state of early earth's atmosphere was?
There are wikipedia pages on Geological history of oxygenation and on Great Oxygenation Event

I don't know much about geology and someone else might be able to give an exhaustive list of evidence (and method of measuring) concerning the oxygen concentration on earth but that would be a very long answer I guess! Rather than a full answer, I give you a list of wikipedia pages below that will interest you and should help answering your own question.


Banded Iron Formation
Evolution_of_dietary antioxidants
Huronian Glaciation
Ice core