As a follow up to What was the formulation of the Bracha about Yerushalayim in the times of the Temple? - In what time period did we start praying Shemona Esrei? (sources)
The Gemara in Megila 17b attributes it to the Anshei Keneses Hagedola, during the times of the prophets. Yoma 69b says that by adding "hagadol, hagibor vehanorah" they brought back that perception of Hashem to the world which was lost with the Churban Bais. So that would specifically place Shemona Esrei after the destruction of the first temple, at the end of the era of the Prophets.
As the Gemara continues (Megila 18a), the text was finalized in the time of Rabban Gamliel in Yanve, which would be towards the end of the Second Temple era - it seems from Brachos 28b that it was together with adding the 19th by Shmuel Hakatan, which would put it a couple of decades or so after the Churban Bais, I believe.