  We expect the monopole signal at the lowest frequencies below $100\,$MHz to
be composed of two components: the deep Rayleigh-Jeans tail of the cosmic
microwave background and two distinct features: the dark ages trough at $\sim
17\,$MHz and the cosmic dawn trough at $\sim 75\,$Mhz. These are hidden under
orders of magnitude brighter foregrounds whose emission is approximately a
power-law with a spectral index $\approx -2.5$. It is usually assumed that
monopole signals of interest are separable from foregrounds based on spectral
smoothness. We argue that this is a difficult approach and likely impossible
for the Dark Ages trough. Instead, we suggest that the fluctuations in the
foreground emission around the sky should be used to build a model distribution
of possible shapes of foregrounds, which can be used to constrain the presence
of a monopole signal. We implement this idea using normalizing flows and show
that this technique allows for efficient unsupervised detection of the
amplitude, width, and center of the Dark Ages trough as well as the
Rayleigh-Jeans tail of the cosmic microwave background for a sufficiently
sensitive experiment. We show that achromatic and smooth response significantly
helps with foreground separation. We discuss the limitations of the inherent
assumptions in this method and the impact on the design of future low-frequency
experiments.
