Exodus Rabah 51:3, (third paragraph in your link)
מהו משכן שני פעמים א"ר שמואל בר מרתא שנתמשכן שני פעמים על ידיהם זהו
שאנשי כנסת הגדולה אומרים (נחמיה א) חבול חבלנו לך ולא שמרנו את המצות
ואת החוקים ואת המשפטים מהו חבול חבלנו לך הוי שנתמשכן ב' פעמים ואין
חבול אלא משכון שנאמר (דברים כד) לא יחבול רחים ורכב לכך כתיב אלה פקודי
המשכן משכן העדות ב' פעמים:
What is 'Mishkan' mentioned twice for? Rabbi Shmuel son of Martha says that it was taken as collateral twice by their hands. This is that Which the Men of the Great Assembly say (Nehemiah 1) 'we have acted very corruptly towards you', this is to say that it was taken collateral twice, and חבול, (corrupt), rather means משכון, (collateral), as it says (Deuteronomy 24), He shall not take as collateral, (יחבול)...
Basically, Exodus 38:21 repeats the word for Tabernacle, משכן, an interpretation of this repetition is that the Tabernacle, by extension the Temple, (our place of worship), was taken as collateral, משכון, (note the similarity in lettering), twice over. A verse from Nehemiah is cited, with this idea being used as an explanation for the two-fold language, חבול חבלנו that is seen there. חבול is a synonym for משכון, collateral, as cited in Deuteronomy.
For our purposes, we see that the Men of the Great Assembly, among them Nehemia, used thisdouble language in reference to thetwo collaterals that would be taken. Given the period during which Nehemiah lived, (just before the building of the Second Temple), it is evident that he and his fellows knewthat there would be a second collateral taken, meaning that the Second Templewas going to be destroyed.
Etz Joseph discusses this explicitly