  The Great Oxidation Event was a period during which Earth's atmospheric
oxygen (O$_2$) concentrations increased from $\sim 10^{-5}$ times its present
atmospheric level (PAL) to near modern levels, marking the start of the
Proterozoic geological eon 2.4 billion years ago. Using WACCM6, an Earth System
Model, we simulate the atmosphere of Earth-analogue exoplanets with O$_2$
mixing ratios between 0.1% and 150% PAL. Using these simulations, we calculate
the reflection/emission spectra over multiple orbits using the Planetary
Spectrum Generator. We highlight how observer angle, albedo, chemistry, and
clouds affect the simulated observations. We show that inter-annual climate
variations, as well short-term variations due to clouds, can be observed in our
simulated atmospheres with a telescope concept such as LUVOIR or HabEx. Annual
variability and seasonal variability can change the planet's reflected flux
(including the reflected flux of key spectral features such as O$_2$ and
H$_2$O) by up to factors of 5 and 20, respectively, for the same orbital phase.
This variability is best observed with a high-throughput coronagraph. For
example, HabEx (4 m) with a starshade performs up to a factor of two times
better than a LUVOIR B (6 m) style telescope. The variability and
signal-to-noise ratio of some spectral features depends non-linearly on
atmospheric O$_2$ concentration. This is caused by temperature and chemical
column depth variations, as well as generally increased liquid and ice cloud
content for atmospheres with O$_2$ concentrations of $<$1% PAL.
