Marie,
Hopefully this will help with your Thread. I think the answer lies in looking at time and distance. Here we would have to include the Gospel of Luke.
If we look at Luke and assume that the “Star” appeared at the moment of Jesus’ birth and it was at this time the Magi observed the start, then it probrably took them time first to gather more information about the possible meaning of the star’s appearence. Something like that didn’t happen over night but most likely took a good period of time.
Once they were able to determine there meaning of the star, that is the “King of Israel” was born, it would have taken an extended period logistically speaking, to organize a caravan to travel west, followed by the actual time it took to travel from where ever they were to Jerusalem.
Then using Matthew, if you knowtice that upon there arrival at Jerusalem they were met with shock and surprize by Herod and his court so it may be reasonable that the star was no longer around and its importance was either dismissed and or forgotten. But an important sign, such as a star was in ancient thought, wouldn’t be something soon forgotten so this presents more reasonable evidence that considerable time had passed.
And a final bit of a hint that some time had passed is the fact that the Magi didnot find the Holy Family dwelling in the stable but in a house. This also shows that there was a time difference between Christ’s birth and the arrival of the Magi. First, housing was available which indicates that the census was over. A census like the one that brought Mary and Joseph to Bethleham was not conducted over a short period of time. Second, to be living in a house there in Bethleham and not Nazarath meant Joesph had to have established himself in his trade and had been working there for a while, otherwise, it would seem logical for Joseph to bring his family back home to Nazarath. Again, I may be assuming too much but I think it would have taken Joseph a good period of time to establish himself in order to remain there.
I am sure you have noticed that I have been very general with my time frame, but that really is what I wanted to present, a general time frame in order to show that a 2 year period is not an unreasonable belief.