Since the question is phrased in the perfect tense, we can't consider the USA of the now. In terms of political conquest, no state in world history has come close, but I would say, if forced, that the Mongols and the Soviet Union were best placed. The Soviet Union was the only modern Universal state...well, it wasn't in the end...but the early years made it out to be so. If things had gone differently, if the 2nd World War hadn't happened, if the attempted communist Revolution that happened in Glasgow soon after the '17 had been successful, the Soviet Union may have remained what it was at the start, an international, supra-national, worker's republic, instead of a 2nd world Russian Empire.
The Mongol Empire was another universal state. The Persian Empire, either under the Persian kings or under Alexander, posed no threat to even a majority of the Eurasian supercontinent. The Mongols did. They were Pagans, and therefore well-placed to bring Buddhists, Christians, Moslems etc under one rule. The Mongols were so superior in military terms to all other people's of their era, that it was merely their own lack of an advanced state system that prevented them from conquering the few remaining unconquered civilizations in the Old World.