There is little evidence to indicate that there were many Christians in the first 2 or 3 centuries of its existence. But after the conversion of Constantine (or, at least his toleration of Christianity) things changed. With one notable exception all future Emperors promoted Christianity. Imperial money was used fund the building of large meeting/worship building and more.
In a new book, published by Oxford University Press, Peter Heather, who is Professor of Medieval History at King's College London, and author of previous books,The Fall of the Roman Empire, Empires and Barbarians, and The Restoration of Rome' links early Christianity and Roman aggression.
And as an aside, its a link that continued into more recent times. When Great Britain fought the two wars with Imperial China in the first half of the Nineteenth century, the treaties which ended those wars, specifically allowed Gt Britain to sell opium into China, but also contained provisions that allowed Christian missionaries into China. And in more recent times our loving brothers in Brooklyn also decided (on occasion) to use the power of the current world hegemon to faciltate the entry of missionaries to some resistant nations.
Hence, its possible to argue that Christianity achieved its position by the power of the sword as much as anything else. So it may also be argued did its Abrahamic twin, Islam.
The book referred to, if the topic interests you is: Rome Resurgent: War and Empire in the Age of Justinian
And for an expanded discussion of what I've referred to above, see this entry in the OUP blog: