Adam Clarke on Ezra 3:1

When the seventh month was come - The month Tisri, which answers to the latter part of our September, and beginning of October. It seems that the Israelites had left Babylon about the spring of the year; that on their arrival at Jerusalem they constructed themselves huts and sheds to lodge in among the ruins, in which they must have spent some months. After this they rebuilt the altar of burnt-offerings, and kept the feast of tabernacles, which happened about this time, and continued to offer sacrifices regularly, as if the temple were standing.