Christmas originally Christ's Mass was not celebrated in the first 300 years of Christianity and after that different churches celebrated it on different dates,
While it is true that Christmas was not initially celebrated, and was later celebrated as part of the Feast of the Epiphany or the Baptism of Christ on January 6th, once the feast was established in the late fourth century, it was set on December 25, and the Annunciation on March 25. All of the Apostolic Churches (the Catholics, the Eastern and Oriental Orthodox, and the Assyrian Church of the East*) use these dates, so there is no divergence in practice. The Assyrians separated from the rest of the church at Ephesus in 431, and the Oriental Orthodox at Chalcedon in 451, so we know these dates are ancient and universal.
Most of the major Christian feasts other than Pascha, the Ascension and Pentecost were implemented in the fourth century. After the Romans stopped killing Christians, it became necessary to develop a liturgical calendar in order to compete with Hellenic/Roman paganism. The Pagan feasts remained popular, and the church had to, as part of its apostolate, draw people away from them. Thus the liturgical calendar was formed, based on an honest reconstruction of historical events, but with the idea being to replace demonic pagan rites with holy Christian ones. Thus Lupercalia was displaced by Candlemas, Sol Invictus by Christmas, and so on. The early English church undeniably used the Feast of All Souls to displace Samhain. I am throughly untroubled by this.
If I were to establish a church specifically for converts from the Islamic faith, I would use minarets rather than bell towers, and serve each of the Hours separately, so Matins would be followed by Terce, Sext, Noone, and then Vespers, forming five daily offices of prayer, with Compline as a sixth office to match the commendable optional late night prayer some mosques have.
At present, Terce, Sext, and Noone (which means Nine, meaning the Ninth Hour, that is, 3 PM) are very seldom served when their name implies. The prayers tend to be grouped together into two or three daily services, typically Matins and Prime, then Terce, Sext and the Divine Liturgy, and then Noone, Vespers and Compline, or some variation on the above. But since Muslims are accustomed to praying on five separate occasions, a Christian mission to Muslims would be best served by following that custom.
Note that I recognize you are a Muslim and offer that example not to cause offence, but to demonstrate the principle of Acculturation that Christianity uses. When we enter a new society we tend to adapt the external forms of our religion to the indigenous culture of that society. We don't always do this; there were some dreadful cases where the Roman Catholics in the 16th century simply imposed the Latin Rite on Native A,ericams without seeking to baptize their culture or teach them Latin. Had it not been for the fortuitous apparition of Our Lady of Guadalupe, I doubt the project would have been a success. I think it's much better when Christianity as it expands seeks to preserve and sanctify the cultures that embrace it.
That said, in recent years the Orthodox have attracted many converts without much of any acculturation because of the beauty of Orthodox liturgical services. The Orthodox Church in America and the Orthodox Church of Japan, to name two examples, both use the vernacular language of their country, but in all other respects preserved the traditions of Slavonic Orthodoxy. There are people who really "dig" some of our worship services. But these beautiful services are themselves the result of acculturation; the Russian style of liturgical music being quite different from the ancient Byzantine chant of the Greek Orthodox, or the music of the Aramaic speaking Syriac Orthodox and Assyrian Christians.