Simply by reading the Bible.
Let me ask you, how did the wisemen know? Didn’t Herod’s scribes verify their story?
Matthew 2
1Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem,
2Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him.
3When Herod the king had heard these things, he was troubled, and all Jerusalem with him.
4And when he had gathered all the chief priests and scribes of the people together, he demanded of them where Christ should be born.
5And they said unto him, In Bethlehem of Judaea: for thus it is written by the prophet,
6And thou Bethlehem, in the land of Juda, art not the least among the princes of Juda: for out of thee shall come a Governor, that shall rule my people Israel.
7Then Herod, when he had privily called the wise men, enquired of them diligently what time the star appeared.
8And he sent them to Bethlehem, and said, Go and search diligently for the young child; and when ye have found him, bring me word again, that I may come and worship him also.
9When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was.
10When they saw the star, they rejoiced with exceeding great joy.
www.biblegateway.com
It seems that the wise men were astrologers of some sort (as you probably already know).
I got this quote from wikipedia:
“In Christian tradition the Magi, also known as the Three Wise Men, The Three Kings, or Kings from the east, are sometimes considered to be Median, perhaps Zoroastrian priests, who were also proficient in astrology from Ancient Persia. The Gospel of Matthew states that they came “from the east to Jerusalem” to worship the Christ, “born King of the Jews”. According to Matthew, they navigated by following a star which came to be known as the Star of Bethlehem.”
I don’t think they would have had access to the Hebrew or Greek scriptures, but I don’t know. The only thing I know is that the Magi were following the Star of Bethlehem:
From wikipedia: The Star of Bethlehem, also called the Christmas Star or Jesus Star, is a star in Christian nativity tradition that revealed the birth of Jesus to the magi (or ‘three kings’) and later led them to Bethlehem.
If you look at verse 5 and 6, the scribes confirm that the Messiah was to be born in Bethlehem, however the scribes would not have known the time of the birth until the Magi told Herod.
Lastly, I just wanted to add, just because one reads the Bible, doesn’t mean he will understand it, or will be able to predict when the prophecies will take place. How could you expect the average Jew to know day or the hour when Jesus was to be born, its not explivitly written. Only God knew the time. Even Mary might not known when the childbirth was to occur, only that she was carrying the Son of God who was to be called Jesus.