See Kasting figure: The rise of atmospheric
oxygen. How do we know?
There are rocks which are 2.5 billion years old
which contain the banded iron formation.
http://www.emc.maricopa.edu/faculty/farabee/BIOBK/BioBookPaleo1.html
These are sedimentary rocks and the redness of the
iron layers indicates that there was oxygen in the water.
Oxygen (O2) was starting to appear in the atmosphere
of the Earth.
After about 2 billion years ago, we no longer see
banded iron formations in the rocks; instead we
see redbeds.
http://earth.usc.edu/~geol150/evolution/precambrian2.html
Redbeds are sandstones which contain iron which has rusted!
This implies (for various reasons) that the amount of free
oxygen -- that is, not in any other molecule -- had further
increased.