Z-dad wrote:
“Alexander the great ruled from 336-326 BCE
Vespasian was roman Emperor from 69-79 CE”
The second Temple was destroyed at about 69 A”Z. If we assume that is was standing for 420 years, as Chazal say, then it was built about 351 BCE.
Shimon Hatsadik was one of the last of the Anshi Kenesset Hagedolah (see Avot, perek 1) which met in the beginning of Bayit Sheni, about 350 BCE. Some years later, I guess around 330 BCE, Shimon met Alexander (Yoma 69a – as we had in the Daf a few months ago).
The history and math works out to prove Chazal.