The gospel tells us that the rabbis in Jerusalem told them the king would be born in Bethlehem. Why speculate when the gospel tells us how the Magi found Bethlehem?
HMMMmmm...
Matthew 2
1 After Jesus was born in Bethlehem in Judea, during the time of King Herod, Magi from the east came to Jerusalem 2 and asked, "Where is the one who has been born king of the Jews? We saw his star when it rose and have come to worship him."
3 When King Herod heard this he was disturbed, and all Jerusalem with him. 4 When he had called together all the people's chief priests and teachers of the law, he asked them where the Messiah was to be born. 5" In Bethlehem in Judea,"Â they replied, for this is what the prophet has written:
6 "But you, Bethlehem , in the land of Judah,
are by no means least among the rulers of Judah;
for out of you will come a ruler
who will shepherd my people Israel."
7 Then Herod called the Magi secretly and found out from them the exact time the star had appeared. 8 He sent them to Bethlehem and said, "Go and search carefully for the child. As soon as you find him, report to me, so that I too may go and worship him."
9 After they had heard the king, they went on their way, and the star they had seen when it rose went ahead of them until it stopped over the place where the child was. 10 When they saw the star, they were overjoyed. 11 On coming to the house, they saw the child with his mother Mary, and they bowed down and worshiped him. Then they opened their treasures and presented him with gifts of gold, frankincense and myrrh. 12 And having been warned in a dream not to go back to Herod, they returned to their country by another route.
Thje king sent them to Bethlehem, but the text does NOT say they found the Christ in that town. It DOES say; however; it was a HOUSE. Luke writes in chapter 2... 21 On the eighth day, when it was time to circumcise the child, he was named Jesus, the name the angel had given him before he was conceived. 22 When the time came for the purification rites required by the Law of Moses, Joseph and Mary took him to Jerusalem to present him to the Lord 23 (as it is written in the Law of the Lord, "Every firstborn male is to be consecrated to the Lord", 24 and to offer a sacrifice in keeping with what is said in the Law of the Lord: "a pair of doves or two young pigeons." 25 Now there was a man in Jerusalem called Simeon, who was righteous and devout. He was waiting for the consolation of Israel, and the Holy Spirit was on him. 26 It had been revealed to him by the Holy Spirit that he would not die before he had seen the Lord's Messiah. 27 Moved by the Spirit, he went into the temple courts. When the parents brought in the child Jesus to do for him what the custom of the Law required, 28 Simeon took him in his arms and praised God, saying: 29 "Sovereign Lord, as you have promised, 33 The child's father and mother marveled at what was said about him. 34 Then Simeon blessed them and said to Mary, his mother: "This child is destined to cause the falling and rising of many in Israel, and to be a sign that will be spoken against, 35 so that the thoughts of many hearts will be revealed. And a sword will pierce your own soul too." 36 There was also a prophet, Anna, the daughter of Penuel, of the tribe of Asher. She was very old; she had lived with her husband seven years after her marriage, 37 and then was a widow until she was eighty-four.[e] She never left the temple but worshiped night and day, fasting and praying. 38 Coming up to them at that very moment, she gave thanks to God and spoke about the child to all who were looking forward to the redemption of Jerusalem. 39 When Joseph and Mary had done everything required by the Law of the Lord, they returned to Galilee to their own town of Nazareth. 40 And the child grew and became strong; he was filled with wisdom, and the grace of God was on him. I infer; from the text; that the flight to Egypt that Matthew recorded came around verses 39-40 that Luke recorded.
you may now dismiss your servant in peace.
30 For my eyes have seen your salvation,
31 which you have prepared in the sight of all nations:
32 a light for revelation to the Gentiles,
and the glory of your people Israel."