Is the "Western Wall" a part of the temple wall that Jesus said would Not have one stone left upon another and if so was he referring ahead to a later time because the chapter is about the end of the age. Therefore, Jesus may have been referring to a time yet to come when the Western Wall would have every stone no longer upon another stone?
During the life of Jesus, and up until A.D. 70, the Temple and the Sacred Enclosure were surrounded by the Soreg Boundary, beyond which non-Jews were not allowed. The Temple included the Sanctuary, the Priests’ Court, the Israel Court, the Women’s Court, the Nazirites’ Court and the Lepers’ Court. The Temple did not include the Western Wall.
Titus, the Roman general, led four legions to besiege Jerusalem and then to burn down the temple. In A.D. 70, after the Temple was burned, the gold in the temple melted in the fire and ran down into the cracks between the stones. The Roman soldiers took the temple apart, stone by stone, searching for the gold, thus fulfilling Jesus’ prophecy in Matthew 24:1-3.
As Jesus was leaving the Temple grounds, his disciples pointed out to him the various Temple buildings. But he responded, “Do you see all these buildings? I tell you the truth, they will be completely demolished. Not one stone will be left on top of another!” (Matthew 24:2 NLT)
Some of his disciples began talking about the majestic stonework of the Temple and the memorial decorations on the walls [of the Temple]. But Jesus said, “The time is coming when all these things will be completely demolished. Not one stone will be left on top of another!” (Luke 21:5-6)
The Temple Mount, where Herod’s temple stood, is now home to the Islamic mosque the Dome of the Rock. The Western Wall stands to the southwest of the mosque and north of an Islamic museum. It was part of the structure of the Temple Mount but was not part of the Temple Wall. Here is a short extract from an article that talks about the history and the significance of the Western Wall:
When the Romans razed the Temple, they left one outer wall standing. They probably would have destroyed that wall as well, but it must have seemed too insignificant to them since it was not part of the Temple itself, just a retaining wall surrounding the Temple Mount. It held no special significance, according to F.M. Loewenberg, until the 16th century when Sultan Suleyman I (the Magnificent) ended nearly 300 years of Mamluk rule and established the Ottoman Empire. Suleyman restored Jerusalem’s city walls in 1536 and encouraged Jews who had been expelled from Spain and Portugal to settle in the city. Loewenberg concludes: ...there is no ancient Jewish tradition that designates the Western Wall as a sacred site. Instead, it was designated as a place of prayer less than five hundred years ago by a Muslim ruler. It took more than three centuries for the wall to attract the Jewish masses and, only in the last 150 years, has it become Judaism’s most sacred site. Yet, even if this place was not intrinsically holy (let alone as holy as the Temple Mount), or even if it had not been so designated by Suleyman the Great, it has become sanctified over time as Jews have increasingly utilized it for prayer. Source: https://www.jewishvirtuallibrary.org/history-and-overivew-of-the-western-wall
In Matthew 24, Jesus’ disciples asked him: “What will be the sign of your coming and of the end of the age?” (Matthew 24:3). What follows is the Olivet Discourse, Jesus’ summary of end times’ events as they relate to Israel. This destruction of Jerusalem was but a foreshadowing of what is yet to come. In the Olivet Discourse, the second half of the tribulation is described in Matthew 24:9-14. More information here: https://www.gotquestions.org/Olivet-discourse.html
Yes, the “end of the age” points ahead in time to when Christ Jesus returns and establishes his kingdom, but this will be a global event. It will affect all the nations of the Earth, and not just one nation. Neither will it be restricted to Jerusalem.