How is it we are able to detect an event that occured ~380,000 years after the big bang?

I can't wrap my head around how we can still detect the CMB. I could if it were a continuous event, but the event that triggered the CMB evolved into matter. Would it not be hidden behind a horizon at this point in time?

If the CMB is a continuous event and we use the CMB to determine the age of the universe, shouldn't that make the age of the universe twice as old as predicted?