From the Bible record we know that:
a) Jesus and his parents lived in a home when the wise men came (Matthew 2:11).
b) Herod had carefully enquired of the wise men when Jesus was born and decided to kill all the baby boys of 2 years old and younger (Matthew 2:16).
Based on this information, we come to the following reconstruction of what happened.
1. One or more wise men saw the unique star.
2. The wise men met with each other and spoke about the star. Depending on where they lived, this happened a few days or weeks after they had seen it.
3. They discussed the matter and decided to visit the newborn king. This may have happened at the very first gathering, but may equally have been several weeks to months later, depending on how important it was to them to visit quickly, their own work situation and other circumstances.
4. They made preparations for the trip. In order to find a suitable time for everyone, their travel date was likely planned several weeks or months later. They needed time to arrange for the gifts, hand over their work responsibilities, prepare the camels, etc.
5. They went to Jerusalem; a journey that took several days to weeks, depending on where they came from.
6. The wise men set out to find the newborn king in Jerusalem. It will have taken several days, before the inhabitants of Jerusalem and king Herod took their claim of the birth serious.
7. They learned from king Herod that the King was born in Bethlehem and them met Jesus.
8. Herod awaited their return, and only after a few days or weeks he realized they had not kept their word.
9. King Herod consulted with his officials and decided to kill all the boys in and around Bethlehem.
So the time that passed between seeing the star and the visit of the wise men took at least a few weeks, but probably several months. Assuming the star appeared at the time of Jesus’ birth, He was already several months old. This fits the fact that Joseph and Maria had found a house to live in in Bethlehem. It also fits Herod’s decision to kill all the boys up to two years of age. If Jesus had been much younger, it would have sufficed to kill the baby boys who couldn’t walk or creep.
On the other hand, Herod wanted to be absolutely sure the king was removed, so he will have played safe. A safety margin of one year would be quite sufficient.
This leads to the conclusion that Jesus must have been at least half a year old when the wise men visited him, but more likely one year.