Not quite.. As we go back in time, the universe was SMALLER, DENSER and
HOTTER. If we go back FAR enough, the universe was so crushingly small and
hot that matter (protons and electrons) and radiation
were coupled. At this early stage, the radiation
could not freely move without being immediately absorbed by
electrons.
When the Universe was about 300,000 years old, it had expanded
and cooled enough that the thermal radiation could finally escape,
a bit like how trapped radiation finally escapes from the surface
of our Sun (only cosmic radiation stays INSIDE the ``sphere'' of
the universe!).
Radiation from our Sun has a Black-Body temperature equal to
the surface temperature of the Sun (5800 K degrees).
Radiation coming from the recombination period
has the Black-Body temperature of the Universe at that time, when it
was 300,000 years old and 3,000 K degrees. This Cosmic
Background Radiation we still see TODAY, but its very cold,
just 2.7 K degrees! This is because the universe
has expanded and cooled over the past 15 billions years!