Matthew 2:9-12

When they heard the king, they departed. And the star which they saw in the east went before them until it came and stood over where the young Child was. When they saw the star, they rejoiced with great excitement. And when they came into the house, they saw the young Child with Mary, His mother, and fell down and worshipped Him. And when they had opened their treasures, they presented gifts to Him: gold, frankincense, and myrrh. But being warned in a dream that they should not return to Herod, they returned to their own country by another route.
Matthew 2:9-12, Modern English Version (MEV)
 
There are several things to note in these verses, the first of which is that it seems perfectly clear that the wise men did not arrive immediately after Jesus’ birth. The most exact we can be about the timing is that it occurred sometime during the window between his birth and when he was about two years old. It also appears that by the time the wise men arrived, Joseph had found more suitable living quarters for his little family.
 
We have to wonder, then were the wise men fooled by Herod? It's not clear, but it did become clear to them after they delivered their gifts. As for those gifts, the three gifts the wise men brought have a spiritual meaning, although it would be difficult to say whether they were fully aware of the prophetic nature of their gifts. Gold is a symbol of kingship on earth, frankincense (an incense) is a symbol of priesthood, and myrrh (an embalming oil) is a symbol of death. Sometimes this is described more generally as gold symbolizing virtue, frankincense symbolizing prayer, and myrrh symbolizing suffering.