Rome somehow figures out a very efficient way to conquer and Romanize Germania. They also develop the Sun cult of Sol Invictus into a proper monotheistic religion that is tied to the State and the emperor and its tenets include conquest and spreading Roman civilization, providing a driving force for further assimilation and conquest of the barbarians. By the time the Huns arrive, the very fortified Limes is on the Oder all the way down along the Carpathians to the Dnieper.
The Huns are defeated decisively, the remnant of their empire get picked up in the following centuries, expanding Rome to the eastern steppes, converting the barbarians to the worship of Sol Invictus which also brings with itself Roman culture, ethos, and innovation. Like Christianity and Islam, it takes many ideas from pagan religions, making conversion easy and fast. The religion spreads beyond Roman borders, and being a worshipper practically means wanting to be Roman. Actual Roman conquest is not so far behind.
The religious militarism drives innovation in the empire towards advancements in military tactics, and engineering, with both the clergy and the state actively supporting and pushing for a technocratic society. To conquer is to be Roman, to innovate is to be Roman. Arabia and Persia are soon crushed and converted, Rome is now advancing into Central Asia. New ship designs allow for the discovery of the Americas, the immense wealth of those lands brings a new golden age and effectively spurs an industrial revolution by 1000 AD (they would not use OTL calendar of course).
The Americas are soon conquered with immense numbers of Romans leaving for the new provinces, which like US territories would get full rights and representation in the Senate, once the population and the level of civilization (as overseen by the church) are high enough. Roman citizenship no longer only applies to a select few, it can be achieved by any
colonia that is accepted as a proper
provincia.
The Mongol hordes soon arrive on the Eastern frontiers, and wreak much havoc along the Oxus and beyond the Urals. Their devastation actually works well for Rome as they get rid of many dissenting elements in recently conquered Persia and among the nomads of the Steppes. The great horde eventually gets defeated in 3 large battles against the Roman legions using gunpowder, muskets and modern military tactics (at this point the are around the military technology of the early 1600s AD). The Mongols retreat beyond the Oxus and the Urals, not making more that meager raids into Roman territories, while the empire consolidates the gains in America(named after a famous cartographer and navigator Americus from Mediolanium).
The empire establishes trading posts all along the now-explored African coast, the South Asian islands and makes inroads into India, conquering its small states one by one by the end of the 1300 OTL. By 1400, the Sun Cult is spread by Roman explorers to said islands, and the dissenters from the newly conquered territories are sent to Australia. The spice islands, the Philippines and Malaya(OTL names ofc) are soon colonized. By 1500, the power of steam allows the spreading of Roman Civilization even faster, and in what is called the Oriental War, the Romans decisively defeat the backwards Ming dynasty of China, fracturing their empire and giving way to the Warlord Era. This helps the empire to spread the Sun cult in the nation and slowly divide and conquer the whole region, making inroads from the great fortress of
Princeps Orientalem in plains to the north, through the great mountains from India, the jungles of Indochina, and of course from the sea. The conversion of the various Chinese states proceeds at a steady pace until the Roman Emperor is proclaimed to possess the Mandate of Heaven.
With the advancement of medicine by 1600 OTL, it becomes possible to make inroads into the deepest Africa, a region yet only partially explored and mapped by Romans. The various tribes are quickly subjected to Roman rule and the Sun Cult is quickly spread among the population, albeit quite forcefully in some cases.
By 1700 OTL, the Mandate of Heaven is proclaimed and the drive for Africa is well on its way, as a large fleet of Roman steamships built of steel arrive at Japanese harbors, with menacing airships looming overhead, demanding the opening of the harbors and subjugation to Roman rule in the name of Sol Invictus.
There you go, as ASB as it gets, but I had fun writing it