Here is a previous comment of mine that may address your question.

Specifically, I would say the 4th century was the defining set of turning points. Demographic estimates put Christian population at around 10% of the Roman Empire towards the start of the 4th century and around the time of Constantine's conversion in the 310s. The Council of Nicaea is not really about Christianity gaining either popularity or power, though it does signify a significant shift in Christianity's relation to Imperial power. By the mid-4th-century estimates tend towards 50% of the population, and much higher by the close of this century, at which time it had become entrenched as the 'official' religion of the Empire, thanks largely to Theodosius I in the 390s.