Masjid Al-Aqsa means the Remote Mosque and refers to the ‘Remote Mosque’ in Madinah, the place where Muslims used to congregate before the Prophet's arrival to the city. Masjid here points to Masjid al-Qabaa in Madinah where it had been established by Muslims of the town.
The famous Masjid Al-Aqsa, the so-called 'Qiblah Awwal', the supposed First Holy Sanctuary, is widely known as Haram ash-Shareef in Jerusalem. But in fact, it was built in 72 AH (691 CE) by the Umayyad Ruler, Abdul Malik bin Marwan, about 60 years after the exalted Messenger passed on. The First Sanctuary was nothing but Ka’bah in Makkah. (See 3:96).
Jerusalem, until the Muslim conquest under the second Caliph of Islam in 637 CE, had been under the control of a few Byzantine Christians for centuries, and there was no person worshiping in a Masjid anywhere in the world but Madinah. So, the question of the presence of a Masjid in Jerusalem during the lifetime of the exalted Prophet should not arise.
Solomon’s Temple had been ravaged and completely destroyed by the Romans (General Titus) in 70 CE. Muslims conquered Jerusalem in 637 CE during the Rule of the second Caliph of Islam, Hazrat Umar Farooq. When he visited the place, he, along with his companions, continued to hold congregations in open grounds although Pope Severinus had given him the key to the City and invited him hold congregations in the Church of Holy Sepulture. Hazrat Umar feared that Muslims might start converting Churches into Masjids, so he politely declined. If a Masjid were present, he would have held congregations there.
The word Me'raaj (physical Ascension) nowhere occurs in the Qur’an. Yet, under erroneous history, it is a popular, though non-Qur’anic, belief among many Muslims that the exalted Messenger was taken up physically to the Skies to meet with God! The Qur’an sets the records straight by asserting that the First ever blessed Sanctuary on earth, the unifying point for all humanity, was the Ka’bah built by Prophets Abraham and Ishmael in Makkah about 2,500 years before Muhammad (S). And since Divine Laws remain unchanged under all circumstances, no human would physically ascend to the heavens. Bodily Ascension is a Biblical and not a Qur’anic theme at all.
Qubbah-tas-Sakhra (Dome of the Rock) in Jerusalem, near Al-Aqsa, was also constructed in 72 AH/691 CE by the same Abdul Malik bin Marwan. Jews wrongly contend that the Dome of the Rock was constructed over the site of the Second Jewish Temple. As mentioned above, it had been ravaged and completely destroyed by the Roman General Titus in 70 CE.
The exalted Messenger never ascended to the heavens. God is everywhere (57:4). The "brilliant" Muslim Muhaddithin and historians produce a lot of irrational and contradictory material on this subject: