Final answer:
Constantine the Great significantly influenced Christianity's role in the Roman Empire, most notably through the Edict of Milan in 313 CE, which granted religious toleration to Christians. However, Christianity did not become the official state religion of Rome during his reign but later in the fourth century.
Step-by-step explanation:
In the early fourth century, Emperor Constantine the Great made significant changes concerning the status of Christianity within the Roman Empire. Though he did not make Christianity the official state religion during his reign, his actions greatly facilitated its spread and eventual dominance. The important year to note is 313 CE, when Constantine issued the Edict of Milan, granting religious toleration to Christians and leading to the end of their persecution. It's essential to underscore that Christianity did not become the official religion of Rome until the end of the fourth century, well after Constantine's rule. Therefore, none of the dates provided in the options—310 C.E, 350 C.E, 302 C.E, or 325 C.E.—accurately represent when Christianity became the state religion.