What was a likely path (and cause, and approx. date)) for the Jews to move from "Israel" to Alexandria?
The city of Alexandria was founded in 332 by Alexander the Great. During this period, the Jews did not exist in a single geographical kingdom of "Israel" but rather were distributed throughout the Levant. Jews were present in the area of Egypt that became Alexandria when the city was founded, and a Hellenized Jewish population has continued to live there until the present. According to Josephus, some areas of the city has a population primarily of Jews, and were allowed a substantial amount of autonomy under the Roman Empire. It was among this population of Hellenized Jews that the Hebrew Old Testament was translated into "koine", a commonly used version of the Greek language, because many members of this population were not fluent in Hebrew, but sufficiently assimilated into Graeco-Egyptian culture to use Greek as their primary language. Philo himself wrote in Greek, as did Josephus.