Yeah that’s part of what I was saying about the imaginary presence of a Greek church. The Greeks lost the whole Canaan area about 200 years before Christ. The notion that they built a church there around the 5th century just doesn’t work. And I’m still saying that building is way to new to match the story about it.
To be clear, Saint Porphyrios Church from the 5th century, was apparently destroyed by Muslims, and eventually rebuilt on the site by Crusaders. The current layout is mostly from the 19th century, presumably possible by bribing some Ottoman grandee.
“Greek” church = Byzantine Eastern Orthodox.
https://en.wikipedia.org/wiki/Byzantine_Greeks
The Byzantine Greeks were the Greek-speaking Eastern Romans throughout Late Antiquity and the Middle Ages.[1] They were the main inhabitants of the lands of the Byzantine Empire (Eastern Roman Empire), of Constantinople and Asia Minor (modern Turkey), the Greek islands, Cyprus, and portions of the southern Balkans, and formed large minorities, or pluralities, in the coastal urban centres of the Levant and northern Egypt. Throughout their history, the Byzantine Greeks self-identified as Romans (Greek: Ῥωμαῖοι, romanized: Rhōmaîoi), but are referred to as "Byzantine Greeks" in modern historiography. Latin speakers identified them simply as Greeks or with the term Romaei.
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Note that there was a Byzantine Church built on the Temple mount that preceded the Dome on the rock. It was of course, seized and converted into a Monument to Mohammad's "Night Ride" to the farthest mosque (Anachronistically, since this supposely happened before there was a mosque and before Jerusalem became a Muslim possession.)
https://orthodoxwiki.org/Church_of_St._Mary_of_Justinian_(Temple_Mount,_Jerusalem)
The Church of St. Mary was a Byzantine church that was built in Jerusalem during the reign of Justinian and dedicated to the Virgin Mary. The church was located on the Temple Mount.
Byzantine historian Procopius wrote that the church was built in 560 AD and burned down by the Persians in 614. Later after the Muslim conquest of the Holy Land, this church eventually was converted into what is the present day Al-Aqsa Mosque.