To understand the verse in question it helps to understand the military context:
ESV Micah 5:
1a Now muster your troops, O daughterb of troops;
siege is laid against us;
with a rod they strike the judge of Israel
on the cheek.
2c But you, O Bethlehem Ephrathah,
who are too little [insignificant] to be among the clans [armies] of Judah,
from you shall come forth for me
one who is to be ruler in Israel,
whose coming forth is from of old,
from ancient days.
a 1 Ch 4:14 in Hebrew
b 1 That is, city
c 2 Ch 5:1 in Hebrew
So the prophet is saying that from the city of David, Bethlehem, the house of bread, which was nothing but a few women and children, the promised ruler of Israel would arise.
But then he says "whose coming forth..." which is apparently taken by the ESV to refer to his birth in Bethlehem. However, (and I'm no Hebrew guru) the word is plural and is rendered in other translations as "whose comings forth" (IE: given the context, "sorties" or "military campaigns").
Now, if I'm correct concerning this then this would be, I believe in a notional sense, similar to this:
[Rom 4:17 KJV] 17 (As it is written, I have made thee a father of many nations,) before him whom he believed, [even] God, who quickeneth the dead, and calleth those things which be not as though they were.
But most important, I believe is the concern in the original question that perhaps the form of one usage of OLAM might tell us the meaning of a similar use. However, that isn't necessarily the case. Context is always the key factor.
The NET Bible renders Micah 5:2 like this:
NET Bible Micah 5:2 As for you, Bethlehem Ephrathah, seemingly insignificant among the clans of Judah--from you a king will emerge who will rule over Israel on my behalf, one whose origins are in the distant past.
That's about all I think we can load OLAM with in actual usage.
And if his military campaigns from OLAM then we must not imagine that his first battle was in eternity past. Surely there was no war on day one!
The point is that the exploits of the Messiah have been in the scriptures from long ago and in God's mind longer than that. To that agree all the scriptures.
I should also point out that interpreting Micah 5:2 as saying that Jesus IS the "ancient of days" clashes with Daniel where the Messiah ascends and appears before God who is referred to as "the Ancient of Days":
[Dan 7:13-14 KJV] 13 I saw in the night visions, and, behold, [one] like the Son of man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him. 14 And there was given him dominion, and glory, and a kingdom, that all people, nations, and languages, should serve him: his dominion [is] an everlasting dominion, which shall not pass away, and his kingdom [that] which shall not be destroyed.