This thing is -270°C and is EVERYWHERE

CMBR is continuously generated by stars and other radiologically active sources,
and contrary to popular belief not a remnant of the Big Bang.

Basically start you Universe at t=0, and go Big Bang.
Now if that event lasted in it's full radiance for a million years,
the signal length through distance would be at best 1 million light years.
It lasted 1 million years and travelled 1 million light years.

Now if you consider that matter can't travel beyond the speed of light,
the matter would have travelled much less than 1 million light years.

Since the origin of the Universe estimated to be 15 billion years ago, in order
for us to receive a signal remnant, we would have to be moving at roughly 0.999999 c,
and I think we'd notice that, in order to still receive part of that event,
otherwise the signal would have passed by in it's entirety well before today.

Radiological celestial object like the Sun, which continuously fissions and fuses,
have as byproduct a radiosignal, which then happens for all stars and other
celestial objects as long as they are still radiologically active.
These signals may have originated from sources which have since 15 billion years
moved far away from the point of emission, and so if you look through a telescope
you'd find no star there.