It is the KING Himself whose origins are ancient, not the king's ancestral line. David's "goings forth" may have been considered "days of old" to Micah, but this phrase can also be used to describe God Himself (who is eternal).
"Days of old" never describes G-d Himself. Check the side notes of your NET Bible to confirm.
Check out common sense too. G-d existed before there ever were "days", so it stands to reason that G-d's beginnings could, by definition, not be from "days of old".
FROM THE NET BIBLE:sn In riddle-like fashion this verse alludes to David, as the references to Bethlehem and to his ancient origins/activities indicate...
The verse, just like the NET Bible states, alludes to David. Nothing more, nothing less. And certainly not an eternal being.