Why did Jesus arrive when he did?

Let's examine this.

The last books of the Old Testament are Zechariah and Malachi which are prophesies.

The New Testament, of course, starts with the birth of JC, or the prophesies of His birth if you're reading Luke, right back to the angel visiting the father of John the Baptist.

The years between the OT and NT include the story of Alexander the Great, who conquered Judea, Egypt and Persia. It is also the time of the first great Philosphers including Socrates, Plato and Aristotle. Ari was, in fact, the teacher of Alexander.

After Alex's death and the collapse of his empire, we see the rise of the Roman Imperator Julias Caeser. Caeser is killed about 30 BC so his nephew Octavian becomes the first real Roman Emperor. At the time of JCs birth he is now Emperor, called Augustus, and Herod is in charge of Judea. By the time JC starts His ministry, Tiberius is Emperor.

Judea is never freed and the Roman Empire does not collapse. Not til the time of Constantine, when he becomes the first Pope. The Catholic church today is basically the decendant of the Roman Empire, and the pope is the Emperor.

(Interestingly, the Pope has usually been Italian. Just before WWII, Polish Cardinal Karol Wojtyla was made the first non-Italian Pope for centuries. When he died in 2005, his successor was the German Cardinal Ratzenberger. Sign of the times.)