The wise men were not at the manger.  They came later. 

1) In Luke 2:21, Jesus was circumcised at 8 days old. 

2) In Luke 2:22-24, Jesus was presented at the temple after Mary’s 40 days of “uncleanness” had passed.

3) In Matthew 2:2, the wise men said they came after they saw the star (“from the east” isn’t a short journey to Bethlehem).

4) In Matthew 2:11, the wise men visited the HOUSE where Jesus was. 

5) In Matthew 2:14, Joseph took Mary and Jesus to Egypt (had to be at least 41 days after he was born). 

6) In Matthew 2:16, Herod killed all the babies under 2, (“according to the time that he had ascertained from the wise men”).