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The early universe before cosmic inflation, was nothing but high energy sub atomic particles. Cosmic inflation kicked in, and dispersed that matter and energy. Cosmic background radiation is the remnants of that process. It comes from all directions in the universe, because it predates inflation.
Which is to say, your question can't be answered, because cosmic background radiation exists only because of inflation. It was created before inflation kicked in, as part of a singularity, with no spatial dimensions. As a result, today, it's everywhere, all the time, from all directions. It wasn't far away when it was created, because far away didn't have any meaning in a singularity without spatial dimensions.