Who first rebuilt the second temple after the Babylonian captivity?
Ezra first rebuilt the second temple when the Jews returned from the Babylonian captivity. This initial structure was makeshift and lacked the beauty and wealth of Solomon's temple. Later, Herod the Great remodeled and enlarged that same second temple, which stood at Christ's first coming.
Les explains that Israel's history includes two past temples and a third yet to come. The first was Solomon's, about 960 B.C. The second was rebuilt first by Ezra as the Jews returned from Babylonian captivity, but it was pretty makeshift because they lacked numbers and accumulated wealth. Later, Herod the Great, embarrassed that it was nothing like Solomon's, began remodeling, extending, and enlarging the second temple. That remodeled temple stood at Christ's first coming and is the one the disciples discussed in Matthew 24.