The operative word in Micah 5:2 is יָצָא (yatsa) means "to go or come out" (see BDB). Therefore, both are correct. The word occurs over 1000 times in the OT and is variously translated as:
- Brought forth, Gen 1:12, 24, 2:10, 15:17, etc
- Go out, Gen 4:16, 8:7, 16, 18, 19, 12:5, etc
- Come from, Gen 10:14, 15:4, etc
If one wanted to translate יָצָא (yatsa) with the same ambiguity, might might say, "proceedings" (which could mean go out or come out), etc.
That Jesus had decided to offer Himself as a sacrifiece of atonement is confirmed here as well as other places such as:
In the case of Micah 5:2, either is possible.
That Micah 5:2 is a Messianic prophecy about the origin of Messiah ("One to be ruler over Israel") is confirmed by the Jewish leadership citing it (and St Matthew repeating it) in Matt 2:6. This prophecy cannot be an ordinary person because the ruler is also described as someone, "One whose origins are of old, from the days of eternity."
Such a description is clearly of Messiah, Jesus Christ. Note this except from Ellicott:
(2) But thou, Beth-lehem Ephratah.—This is a passage of immense
significance, through the interpretation given to it by the chief
priests and scribes in the Gospel of St. Matthew. Beth-lehem Ephratah:
the two names, modern and ancient, are united, each of them having
reference to the fertility of the country. In the Gospel the scribes
quote, evidently from memory, the passage from Micah, in reply to
Herod’s question; and their first variation is in the title of the
town—“Thou, Beth-lehem (not Ephratah, but), land of Judah.” So also
the people protested against Jesus on the ground of His being from
Galilee, for, “Hath not the Scripture said that Christ cometh of the
seed of David, and out of the town of Bethlehem, where David was?”
All the other commentaries say something very similar in https://biblehub.com/commentaries/micah/5-2.htm - too much to reproduce all the wonderful material here.
- 1 Peter 1:20 - He was chosen before the creation of the world, but was revealed in these last times for your sake.
- Rev 13:8 - All inhabitants of the earth will worship the beast--all whose names have not been written in the Lamb's book of life, the Lamb who was slain from the creation of the world.
- Heb 9:26 - Otherwise Christ would have had to suffer many times since the creation of the world. But he has appeared once for all at the culmination of the ages to do away with sin by the sacrifice of himself.