Christianity first came to the Roman Empire in Jerusalem as a Jewish religion during the 1st century AD. Christianity emerged outside Jerusalem in Antioch and then Alexandria before eventually touching upon nearly all parts of the Empire. The religion was at first allowed to flourish without punishment from the central government for the most part. Under the Emperor Nero, however,
"punishment was inflicted on the Christians, a class of men given to a new and mischievous superstition" (superstitionis novae ac maleficae).
The civil war that occurred during Nero's reign was in part blamed on the Jews, since Christianity was basically considered a "Jewish sect." Christianity became more widespread during the 4th century when Constantine I (324-337 A.D.) became the first Christian emperor. Christianity became the official religion of the Roman Empire under the rein of Theodosius I in 380 A.D.
This depends on what you mean by "emerge." Christianity, of course, began to spread soon after the death of Jesus around 33 CE. The faith spread and grew and eventually came to be accepted by the Roman emperor Constantine in the early 300s. We might say, then, that Christianity went through a process of emerging and growing during the 300 years between 33 and around 330 CE.
Christianity began to spread soon after Jesus's death. The most important figure in this spread was Paul the Apostle, who was martyred in Rome around 67 CE. This shows us that Christianity had spread by that point to the extent that it came to the attention of the leaders of Rome.
The message of Christianity was spread around the Roman Empire by St. Paul who founded Christian churches in Asia Minor and Greece. Eventually, he took his teachings to Rome itself. The early converts to Christianity in Ancient Rome faced many difficulties. The first converts were usually the poor and slaves as they had a great deal to gain from the Christians being successful. If they were caught, they faced death for failing to worship the emperor. It was not uncommon for emperors to turn the people against the Christians when Rome was faced with difficulties. In AD 64, part of Rome was burned down. The Emperor Nero blamed the Christians and the people turned on them. Arrests and executions followed.
Christianity actually began during the life of Jesus Christ somewhere around 27 C.E. It began as a small Jewish sect around the eastern Mediterranean, in Judea, which had become a Roman province in 6 C.E.
Christianity quickly spread through the teachings of Christ’s disciple, Paul. Paul used the advances in Roman Empire to travel to the empire’s most important cities.
Christianity was often misunderstood and its followers were often persecuted by Roman leaders. Emperor Nero used the Christians as a scapegoat after the Great Fire of Rome in 64 C.E. Regardless of the persecution, Christianity grew rapidly and became the dominant religion of the Roman Empire.