Universe not expanding after all?

Maybe I’m missing something obvious, but in a steady-state universe why would there be a CMB at all? I can’t think of any explanation for such a uniform, isotropic source of radiation other than the universe being hot and dense in the past.

One explanation for the CMB in a steady-state universe I recall (due to Fred Hoyle, I believe) was that the light of old stars might be scattered by peculiar needle-shaped grains of iron, but I don’t think this is in line with modern precision measurements anymore (but you’re right to note that the CMB is a great problem for all steady-state theories, being often considered the ‘smoking gun’ of the big bang, to mix some metaphors).