Once again, we do not know when this year was. It could be during the reign of Cyrus but is more likely to be during the reign of Darius. Since we are not told the precise year, we know that the focus is on the month in which these events took place. The second month in the Jewish calendar is known as Ziv.1 This month would be in spring (April-May).2 Spring is the beginning of the dry season and would thus be a good time to begin building. Work on the first temple constructed by Solomon also began in the second month (1 Kings 6:1).
8 Now in the second year after their coming to the house of God at Jerusalem, in the second month, Zerubbabel the son of Shealtiel and Jeshua the son of Jozadak made a beginning, together with the rest of their kinsmen, the priests and the Levites and all who had come to Jerusalem from the captivity. They appointed the Levites, from twenty years old and upward, to supervise the work of the house of the LORD.