An earthquake in Our Time Line does not occur as it did in ~1800 BCE. As a result, the Ghaggar Hakra river system does not shift. As a result, the Indus Valley Civilization centered around Dholavira survives strong for centuries or millennia longer. As a result, there are stronger trade relations between China and the west, and the IVC grows strong on their part of the trade triangle.
Here we deviate from the fairly-certain dominoes of fate and venture into far more subjective game... possibly Jenga.
The increased trade and specialization could provide demand and wealth to drive alchemy in the far east. Chinese alchemists might therefore develop things on an accelerated time-table. The very earliest reference to something that could be gunpowder date to 140 CE, but in OTL it took until 1044 to get the basics, and saltpeter wasn't refined until ~500. Let's say that the early references are correct and that the merchants pick up on the idea of sparking powder quickly, and that in a matter of a hundred years gunpowder as we know it is developed.
If we delay the earthquake and Ghaggar Hakra river shift to around this point, then the IVC would undergo a massive catastrophy right as the Roman Empire gets gunpowder (even as it undergoes its crisis in the third century, assuming that there's no butterfly-effect changes of a strong Indus civilization). If we want an Empire with Rifles then we can say that whoever was in change at the time was a visionary who saw what gunpowder could do and turned the first firecrackers he got into charges for cannons.
Such a figure would have to overawe the other claimants to the Imperial throne - something he may do by proposing a return to expansion in the east, now that he has given four prototype cannons to the army and (less spectacularly and more importantly) the IVC is wracked by famine and drought following the rivers shifting.
This new unifying Emperor drives east, loots the storehouses of Dholavira of gold, lapis lazuli, and gunpowder, and returns to Rome to shore up the fracturing country. The savages of the north did not take part in trade and thus have no source of gunpowder, and even if they had the formula, they have no real industry to produce it. Roman defenders, if they have any inventiveness at all, will soon create the landmine and start the process of miniturizing cannons - if they don't borrow the crude Chinese flamethrowers directly!
We've now removed Constantine from the timeline and put a new Caesar on the throne firmly in Rome. We've given him cannons and bombs against the Visgoths, and we've set them on the course to rifles.
Pick an era after that and decide how Roman you want to be and ho many guns you want to have, and you can probably come up with a justification for that. Rome could still fall, leading to a very different high medieval era with marksmanship duels instead of jousts, or a fantastic eternal Rome of the 17th century armed with rifled, scoped, precise longarms, marching East once more....