I'm working on an alternate history book based on historical events. Basically, the group of tribes from the Roman era that are grouped under the Belgae group managed to avoid being conquered by the Romans, remained a nation during the Germanic invasions at the end of the Roman Empire and then started forming a global empire. Basically, take the below map (courtesy of Wikipedia), but everything between the English Channel, Paris, the Rhine and the Moselle is not part of the Franchi, but part of this Belgae nation:
After this time, any time someone born in an area part of Belgium at the time of birth went on to conquer another region in our timeline, that region would remain a part of Belgium permanently and would never be conquered again by any other nation, nor would any rebellions or other nations rise in that area.
Now, my knowledge of historical events is not that good, but I did find that the Merovingian dynasty and the Carolingian Dynasty were born right in the middle of that region, which means that Belgium would rather quickly have control over France and the Holy Roman Empire. Add to that the Reconquista, the invasion of England by Normandy and the Crusades. From what I can tell, most of Western and Central Europe would have been part of Belgium by the 1400s. This means that all colonies also would have become part of Belgium.
I'm not sure how much of the world would be part of the Belgian Empire. That is the biggest blind spot in the story right now: what areas were not conquered or colonized by a power recursively located in land once ruled by someone who was born in the Belgae tribe area? From what I can find, China, Japan and Korea are the most prominent in this category. I'm not sure about Russia: it has been invaded multiple times, but as far as I know, none of those invasions had any real success, with Russia fighting a war of attrition and retreat until the invaders were forced to pull back.
I see that many people among you comment on how certain aspects of my question are extremely unlikely, like the fact that noone revolts against the Belgians, or that the Belgians wouldn't work like that because they don't share an identity, or that this is a question about alternate history and thus shouldn't belong here.
About the alternate history part: I'm not asking about alternate history. I'm asking about how the actual history of our world goes so I can build a better backstory to my book, because many of the events in our world also happen in the book, just with different countries. For example, the Crusades still happen. So do the Colonial periods, the Mongol Horde and the Viking invasions. the only difference with out world is that some of the later crusades to reconquer lost holy land don't happen, the Colonies don't become independent and the invasions fail at the border of the Belgian empire.
The rebellions and uprisings: I worded that badly. They do happen, but they're struck down rather fast. There are no sucessful rebellions or uprisings.
Belgium not working like that: In the book, Belgians have a unique feat called Ancestral Guidance (https://worldbuilding.stackexchange.com/questions/9932/what-consequences-would-ancestral-guidance-have) which gives them an edge over other groups and gives them an identity. This feat is hereditary and rapidly spreads to newly conquered regions, while not going anywhere beyond the border.