...and if they had any comprehension of Daniels 70 week prophecy, they would have been looking out for signs!
In 3 BC on the new moon of the Jewish seventh month Tishri (that is September 10/11 on the Julian calendar) the wandering king star Jupiter conjuncted with the king star Regulus in the king constellation Leo. And after passing Regulus because of retrograde motion Jupiter returned to conjunct Regulus again before turning for a third conjunction. From the earth this would look like Jupiter crowning Regulus.
And there is an old prophecy where Jacob blesses his sons and with prophetic imagery describes this astronomical or Star of Bethlehem event.
Genesis 49 9 "Judah is a lion’s whelp;
From the prey, my son, you have gone up.
He bows down, he lies down as a lion;
And as a lion, who shall rouse him?
The scepter shall not depart from Judah,
Nor a lawgiver from between his feet,
Until Shiloh comes;
And to Him shall be the obedience of the people."
When the wise men visited king Herod in Jerusalem looking for the newborn King of the Jews they explained to Herod that this event or the star first appeared in the autumn of 3 BC. And then they went to Bethlehem and saw the star again over the town.
With astronomy software we can see the movements of the planets anywhere anytime... and on December 25 2 BC on the way from Jerusalem the planet Jupiter is over Bethlehem on a moonless night. And of course they found baby Jesus there and worshiped Him with gifts consisting of gold myrrah and francensine.
So we can know for an absolute certainty that Jesus was born somewhere between September 10 3 BC and December 25 2 BC.