This is an AU where Jesus never came down to Earth / the urban legend of Jesus stayed an urban legend and didn't form a cult.
This AT would remain mostly the same until the Western Roman Empire collapses at the hands of the Visigoths and Huns. The Eastern Empire was headquartered at a city which was named Constantinople in OTL but since there was no Christianity for Constantine to make legal, the city retained its original name: Byzantium (hence the Byzantine Empire).
The Jewish revolt would have still occurred in 70 AD and they would have been spread out across the empire as a result of their failure. In this timeline however, Jews would often get seen as barbaric because monotheism was very foreign to the Romans who held many gods.
Byzantine Empire (New Roman Empire)
Without Christianity, monotheism would have likely not been popular enough for Islam which was mainly founded on Judaic ideals. The Byzantine Empire took a percentage of the territory once held by the Roman Empire under Justinian the great (6th century AD) like in OTL. Without Islam to cause a caliphate, the Byzantine Empire would remain unrivaled in Southeastern Europe, the Levant region, and North Africa. By 900 AD, the empire expanded northwards to encompass the rest of what once was the Roman empire. At that moment, the Byzantine Empire was renamed the second roman empire.
Despite the lack of Ottomans, the Mongol Invasion did take most of present day Turkey and part of Iraq. Although Mongke Khan died before they could take Byzantium, it was a sign of the Roman Empire's vulnerability. Eventually, the Mongolian Empire split into several pieces; the area which the Romans lost was part of the Ikhanate. An attempt by the Romans to retake their lost territory in the early 1300s failed. Around this time, however, they finished off the vikings after two previous wars.
The black death had a detrimental effect on the empire. The plague was viewed by the Romans as punishment from the gods for straying away from religion. As a result of the black death, the Golden Horde was weakened. Although the black death devastated the Roman economy, it did not disrupt the roman lineage. This was not the case for the Ikhanate where Abu Said (the leader) and his sons died; this led to the disintegration of the Ikhanate. The black death killed a third of the empire's population.
After the plague was over, the wealth belonging to dead individuals was inherited.
The vikings typically traded with European tribes and were enemies of Rome, much like the Carthaginians. In the roman expansion period, they lost much of their territory in continental Europe to the Romans which led to the 1st Nordic war. The Romans had superior technology, especially in sea battles when they had Greek fire (could not be put out by water) whereas the Vikings' ships were mostly meant to transport troops for land invasions. The second Nordic war occurred after the mongols halted their expansion; the Vikings saw weakness in the Romans and attacked Continental Europe in 1255. However, they were soon proven wrong when they lost Denmark and had a blockade put over present day Norway and Sweden three years later. In 1271, Roman Emperor Michael VIII Palaiologos launched a final campaign against the vikings, ending a few years later with a roman victory.
In the 1400s, the Roman empire decided to form colonies outside of their dominion and explored the indies.
Rise of Russia
Ivan III united the Slavs against the Golden Horde and made Russia an independent nation and because the first Czar. Ivan IV (the terrible) expanded Russia westward to encompass present day Ukraine and Belarus as well as the Baltics. The Romans saw Ivan's expansionism and invaded Russia with about three-fourths of its army in 1553. This invasion ended in failure due to Russia's harsh winters with only a third of that invasion force surviving after retreating.
Decline of Rome
Out of retaliation for the failed invasion, Ivan the terrible expanded westwards and took roman territory in OTL Denmark and Germany. Ivan was very cruel to the Romans conquered by the Russians with many men being slaughtered, woman being raped, and children being indoctrinated to fight for Russia. As a result of losing much territory to Russia, the roman empire lowered its military age to make up for losses. Most of the men who weren't killed were almost immediately drafted into the Russian military. By Ivan's death, rome had fallen and the empire was on its last legs. Future czars finished the job and brought the fall of Byzantium with the city being renamed Ivangrad.
Golden Age of Russia
Russia had control over all of continental Europe which was more beneficiary to Russia than in OTL when they got Siberia.
Russia's first colonies were in the West indies