Do you have any evidence that Muslims have only "recently" started to claim it is in Jerusalem? From what I understand, they were already claiming that well over 1000 years ago.

> The night journey is said to have happened in 621, but the Al-Aqsa Mosque was built in 637 when the Muslims captured Jerusalem. So the Al-Aqsa Mosque of the Quran is not the one currently called the Al-Aqsa Mosque.

Standard explanation for this: "Al-Aqsa Mosque" has two senses, a broad sense and a narrow sense. In the broad sense, it is the entire complex of Islamic religious structures on the Temple Mount, centered on the Dome of the Rock. In a narrow sense, it is the main congregational prayer hall in that complex, the current building of which was constructed in the 1030s. The 637 structure you mention was a temporary wooden structure, which by the next century was replaced by a much grander stone one, which went on to twice be destroyed by earthquakes.

So, since in the broad sense "Al-Aqsa Mosque" means the whole Temple Mount complex, of course the Temple Mount pre-existed the Islamic conquest of Jerusalem in 637 (around 5 years after Muhammad's death), and it was there for Muhammad to have supernaturally visited in 621 (if one believes he went on such a supernatural journey, I personally don't)