When was Al-Aqsa Mosque built, and is it possible for the Prophet, peace and blessings be upon him, to have been carried on the Night Journey to a place that did not yet exist?

The Aqsa Mosque was built after the death of the Prophet, peace and blessings be upon him, as a renovation, not as a new foundation. After Solomon, peace be upon him, built it, Nebuchadnezzar destroyed it, then it was rebuilt, then Titus destroyed it, and it remained so until the Muslims built it. What the Prophet, peace and blessings be upon him, was carried on his night journey to was the place of the mosque, and it was called a mosque because its site remains a mosque even if it is demolished.