Even if China or some African nation rose to such worldwide prominence early (certainly within the realm of possibility), the communication and logistic hurdles would prevent an entire world under one flag (as required in the OP). Look at Rome: a dominant power in its day, its sheer size required it to be split for administration purposes. And didn't even control all Europe, much less the world. The technology barely exists now, if at all.
EDIT: Come to think of it, China is still a Eurasian country, so it doesn't fit the OP anyways.
I was responding to someone who said that an Eurasian country couldn't do it either: and I said "in the modern era", by which I didn't mean the _early_ modern Era, but the era which involves things like steamships, telegraphs, and other stuff fourth century Rome lacked....
(Not that I consider that a particularly likely scenario: why should be money and effort be spent civilizing a bunch of barbaric roundeyes? If they want to be civilized, they should come and learn.)
Bruce