When in history did Purim happen? I understand that there are several opinions that this is based on (who אחשורוש was, whether this was before or after the end of the exile), but I've been unable to find the sources related to it.
From Codex Judaica pg. 112: they started to rebuild the Second Temple in 3391 Jewish year (-370) Achashverosh the second made his banquet in the year 3395 (-366). In the year 3406 (-355) Mordichai proclaimed the celebration of Purim.
Rabbi Yehuda Landy wrote an in depth book (Purim and the Persian Empire) about which Achashverosh was part of the Purim story,and has many archaeological pictures and finds which help determine who and what.
The story of purim happened about 70 years after the destruction of the first temple which happened around year 422 BCE
According to purely Jewish sources, as elucidated by seder olam rabba, Achashverosh lived before Darius the Great, hence purim took place after the beginning of building the temple (during Cyrus) and before it was finished.
Taking into account other historical records it seems that Achashverosh was Xerxes, after Darius the Great, in which case purim took place after completing the Temple.
Both can be read into the pshat of Tanach.