I guess you mean, the people living there were Muslim like they are now? Well back then they were mostly Christians already. There were other religions there too - there were still some Jewish people there, for example, but most of them were kicked out of the region after they rebelled against the Roman Empire in the 1st century. But during the time of the Byzantine Empire, Christians already lived natively in the Middle East, as they had for hundreds of years.

There weren't any Muslims there until the 7th century. But even after they took over the Middle East from the Byzantine Empire and from Persia, there were still lots of Christians there. Christians were probably the majority of the population for a long time after the 7th century. There are still Christians there now, all over the Middle East.