How? I don't know, considering this stretch to area probably is one of the most divided places on Earth, but you have to combine ALL of continental Europe together into one country. As a bonus, try to include the British Isles in this country too.
Now, GO!
Is the Scandinavian Peninsula included? It isn't directly connected to the rest of continental Europe in a straightforward way - Only through Russia, which you say isn't necessary to the challenge. It's hard to imagine the Romans or the Franks getting as far as Lapland - Why would they go through all the trouble?
When Charlemagne dies he has only one son and his kingdom remains intact. Being Holy Roman Emperor means exactly that. His descendants slowly conquer Europe while also spreading the Christian faith. By say 1400 all of Europe is united; one faith, one nation, one emperor.
You don't just need a long succession of single sons. You need an endless succession of Charlemagnes. Daesna happen.
No, Russia isn't included.
No, Russia isn't included.
Isn't kind of happening now? It just depends on who will control the E.U. the French or Germans. A United States of Europe would not include the U.K.
And related to this is the longevity of empire issue. Europe developing like China did would need a POD changing it beyond recognition. The Roman Empire is an entirely different kind of big blob. It simply is not going to be a Chinese style empire.