Chance and Certainty
No one thinks it is a mystery that Jesus Christ was born in a specific place at a certain time of history; they think it is by chance.
If you believe in accidentalism and fatalism, while neglecting causality and logicality, a question such as why the Messiah was born at a certain time may not be your concern. However, you may still live under holy certainty supported by holy causality and logicality.
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Specifically, in a generation after the well-known episodes centered on relationships between Cleopatra, Caesar, and Antonio, Jesus Christ was born.
(Why was not Jesus Christ born in Rome or Egypt to make things settled at one dash, for example, by taking charge of the Roman Empire and Cleopatra at the same time?)
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King Herod's father went out to see Caesar and got his support for governing Judea.
King Herod himself after assassination of Caesar went out to see Antonio and Cleopatra in Alexandria and further went to Rome to get Rome's support for governing Judea.
King Herod himself after death of Antonio and Cleopatra swore loyalty to Octavius (Imperator Caesar Divi Filius Augustus) who became the First Emperor of the Roman Empire.
And then, during the last years of King Herod of ancient Israel, Jesus Christ was born among Israelites according to prophets of Daniel or God's promise to descendants of Abraham.
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I do not think that God chose that time by chance.
1) King Herod, as a representative of descendants of Abraham, completely forgot glory of his tribe, more than fully surrendering to the Roman Empire.
2) The Roman Empire had its first Emperor, which indicated a change in a certain character of the empire that could not make the world any safer. An Emperor in Rome vs. the Messiah in Jerusalem seemed to well match, though from a human point of view.
3) As Jesus Christ never mentioned Pyramid, Cleopatra, and those drastic wars fought in the eastern Mediterranean just preceding His birth, it is apparent that He did not like those historic events and monument.
You have to explain an implicit relationship betweeen Cleopatra and Jesus Christ, not between Mary of Magdala and Jesus Christ, as the sequence of events was clearly connected around true A.D. 0 or the so-called 1 minus.
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For Jesus Christ to be born at the age itself saved the world under the threat of destructive civilization of the Roman Empire.
It even paved the great way for future birth of Islam 600 years later which succedded in suppressing mighty Persia.
It even enabled Japan, the only Imperial country in the world today, though nominally, to emerge 1900 years later.
It might even make possible your success where Cleopatra failed.
"SHAKE THE DUST OFF YOUR FEET"