The centre of monotheism in Palestine was Bait-ul-Muqaddas whose construction was started by Prophet Daud (AS) and completed by Prophet Sulaiman (AS). It was destroyed in later years twice (if my memory serves me right) and the only remnant left of that original building is the famous wailing wall.

The Aqsa mosque was built later by Muslims after Palestine was conquered in the time of Umar (rta). Jews claim that some of the original foundations of Bait-ul-Muqaddas have been overlapped by this mosque.

That place has a sanctity as a chosen land of God. The presence or absence of a physical mosque has a secondary value. The land is the mosque chosen by God himself. Those two lands were chosen as center of monotheism. Mosque is a symbol of that decision. Even if there was no mosque physically present at that time, it doesn’t make a difference. That dream was a symbol of transferring custodianship of both mosques to Prophet Muhammad (sws). Termination of rank of Shahdah for Bani-Israel and giving this duty to Bani-Ismael.

Since Quran is very explicit about re-building of Kaaba at the hands of Prophet Abraham (AS) and Prophet Ismael (AS), there is no such explicit details (not to my knowledge) on when was the first mosque built there and whether any first mosque was built by Abraham (AS) himself or not, there is no such thing mentioned. Therefore, we rely on Jewish history in this regard. But we know that Bani-Israel were formally settled In Palestine after rise of Prophet Moses (AS), therefore it is highly probable that first proper structure was built later by Prophets Daud (AS) and Sulaiman (AS).