We were discussing construction dates of the major buildings at Temple Mount/Haram al-Sharif and wished to know the dates for the Church of the Holy Sepulcher and the al-Aqsa Mosque.
The Church of the Holy Sepulcher’s initial construction date is known to be 326 CE under Constantine the Great, the Roman emperor at the time, with the Church opening in 335 CE, though construction would still continue past Constantine’s death (of 337 CE).
Source 1: https://www.jstor.org/stable/3655081
Source 2: https://www.jstor.org/stable/546508
The al-Aqsa Mosque’s exact initial construction date is not known, but scholars believe it was initially constructed between 688 CE and 692 CE by ‘Abd al-Malik, the reigning Umayyad caliph. Evidence shows that it may have only been started under him and been fully constructed, or expanded, after his death by his son al-Walid I in 715 CE (as ‘Abd al-Malik had died in 705 CE).
Source 3: https://www.jstor.org/stable/1523262
Source 4: https://www.jstor.org/stable/1523257