Both the Quran and Jewish scripture refer to the destruction of Masjid al Aqsa, known as Solomon’s Temple to Jews. In the Quran Allah tells us that He warned the Jewish people in earlier scriptures that they would be punished and overcome twice because of their disobedience to Him. You can refer to Surah al Isra of the Quran to read some relevant ayaat (verses). Scholars of the Quran state that the first of the times Quran refers to was when the Babylonians sacked Jerusalem in the 6th century BC. They destroyed the temple built by the Prophets Dawud and Sulayman (Masjid al Aqsa to Muslims, Soloman’s Temple to Jews). Scholars say the second time the Quran refers to is when the Romans flattened Jerusalem in 66 AD under General Titus. The Romans destroyed the temple which had been rebuilt after its first destruction (the so-called “second temple”).
The first of the two warnings mentioned in Quran can still be found in the present day Torah- in the books of Yasayah, Yarmiyah, Hizqeel and Zakariya. This warning in their own scripture shows it was the will of God that the original Masjid Al Aqsa (‘Solomon’s Temple’) was destroyed. Both Jews and Muslims believe that God is more powerful than any human army, so if God had willed to save the Masjid/temple from the Babylonians or the Romans He could have. But He did not. This is important to understand in the history of the masjid/temple, as you refer to it. It has never been rebuilt by Jewish people since.
Muslims believe in all earlier Prophets of Allah (God) and also that Prophet Muhammad (peace be upon him) is the final Prophet of Allah. So when they conquered Jerusalem in 637 AD under the Caliph Umar (may Allah be pleased with him), the Muslims rebuilt the masjid originally built by Prophets Dawud and Sulayman. This is the building which is known as Masjid al Aqsa today, which some Jews are now trying to demolish. The Muslims did not demolish any buildings as there was nothing there.
And the problem is that Israel's governments, its courts and its police shore up this theology, fanciful and whatever, by denying Jews free access and free worship, rights guaranteed by law, and provide backing for institutional discrimination.