Much meaning is attached to electromagnetic waves that stream into earth (and the solar system area). Among the meanings is that these waves represent heat in the CMB. There is good reason for this, because we know that these waves (at least where we observe them here on earth and area) do represent heat.
However, since we have only seen the quanta (photons) in our time and space here, it would be wrong to assume that this represents the same thing far out in unknown space and time.
After all they calculate radiant energy using time.
"radiant energy may be calculated by
integrating radiant flux (or
power) with respect to
time"
Radiant energy - Wikipedia
Additionally we have only seen these oscillations of electric and
magnetic fields here at our point of observation (The fishbowl of earth and solar system area).
Light has only bee seen here, so the speed that it moves here in our time and space is all we know. If space and/or time were different in far space then these oscillations and fields and etc could not be assumed to represent the universe at large. We may better think of it as representing how light and waves and fields operate/exist HERE in the fishbowl.
Therefore the cosmic microwave background might not exist as we thought, but could just be how we see light and fields and waves in time and space here.
In this case it cannot be used as evidence for any big bang. The only question is therefore...do we KNOW that time exists the same out there (and space) or not?