Why did the early universe become transparent only after 380,000 years?

In the early universe, temperatures were so high that atoms could not survive; matter existed as a plasma of free electrons and nuclei. Light bounced off these charged particles, making the universe opaque, much like the inside of the Sun. As expansion cooled the universe, electrons and protons combined into neutral hydrogen in a process called recombination. With far fewer free charges to scatter photons, the universe became transparent. The radiation released at that time is what we now observe as the cosmic microwave background.