The radiation cannot pervade through the early universe, just as optical light is hindered by dense fog.
Only 300,000 years later free moving electrons started being trapped by nuclei, to form the first atoms. Astronomers call this phase the recombination era.
In the animation the sinking temperature is illustrated by a blackenig sky. Electrons (pink) are trapped by nuclei (green). Radiation (white) can feely travel through the universe.