We know "the star they had seen when it rose" was seen 2 years earlier, since Herod ordered the massacre of the boys 2 years old and younger according to "the time which he had diligently enquired of the wise men." We also know the star is the one spoken of by Balaam....
"I shall see him, but not now: I shall behold him, but not nigh: there
shall come a Star out of Jacob, and a Sceptre shall rise out of
Israel."
This is Balaam's 4th oracle in Numbers 24. It comes from the mouth of Balaam but is the word of the Lord as given by God. For some reason, God chooses to speak a prophecy of the coming Messiah thru Balaam who is serving as God's "donkey". Not only is the scepter to come out of Israel, a more specific prophecy is given by Jacob concering Judah in Genesis 49:
The sceptre shall not depart from Judah, nor a lawgiver from between
his feet, until Shiloh come; and unto him shall the gathering of the
people be."
We also know from Isaiah 9:
"The people that walked in darkness have seen a great light: they that
dwell in the land of the shadow of death, upon them hath the light
shined."
We know from Micah:
"But thou, Beth-lehem Ephratah, though thou be little among the
thousands of Judah, yet out of thee shall he come forth unto me that
is to be ruler in Israel; whose goings forth have been from of old,
from everlasting."
The "Star of Bethlehem" has now been revealed to the wise men, magi, kings who understood with faith in these and other prophecies. The timing of the coming star was also understood as wisdom had been given to Daniel in chapter 9 about when the Anointed One would come and this understanding was obviously given by God to these men 2 years before Christ's birth in flesh.
Christ Jesus is the "Star of Bethlehem".
Christ Jesus "is the first born of creation."
Christ Jesus is the "light of the world."
In this most majestic event of all time, God planned and orchestrated the Star of Bethlehem to lead and display with pin-point accuracy the arrival of his only begotten with an intersection of earth's creatures centered over a manger where lay manna from heaven for a starving world:
"I have installed my king on Zion, my holy mountain." I will
proclaim the LORD's decree: He said to me, "You are my son; today I
have become your father."
(Psalm 2.6-7) God used the Star of Bethlehem to signal this day---the day Jesus was born.