Analysis of information sources in references of the Wikipedia article "Σημαίες της Οθωμανικής Αυτοκρατορίας" in Greek language version.
[...] the crescent [...] appeared on the standards of [Ottoman] infantry under Sultan Orhan (1324-1360)
The city of Byzantium, also known as Constantinople and, in modern times, as Istanbul, was dedicated to Diana, goddess of the hunt, and the crescent was the symbol of Diana. In 330 AD, the Emperor Constantine rededicated the city to the Virgin Mary whose star symbol was added to the previous crescent. When the Turks took possession of Constantinople, they found many crescent flags and adopted the crescent as a symbol of the Ottoman Empire in about 1453 AD.
The city of Byzantium (later known as Constantinople and then Istanbul) adopted the crescent moon as its symbol long before the birth of Islam. [...] When the Turks conquered Constantinople in 1453, they adopted the city's existing flag and symbol.