Historically deepening ‘interaction capacity’ – or inter-polity connectivity – has formed a crucial pre-condition for the emergence of a truly global politics. Who drove increases in interaction capacity, how did they do so, and for what purposes? This paper contends that IR lacks a convincing answer to these questions and responds by theorising the role of private infrastructure builders in the making of a global international system. Focusing on three examples of ‘infrastructural vanguards’ – 17th-century company-states, 19th-century submarine cable companies, and 21st-century platform companies – we trace the globalisation of world politics through these actors’ creative responses to what we term the problem of connectivity under anarchy. By overcoming technical-administrative, commercial, and political barriers associated with intermediation at a distance, we show that infrastructural vanguards were key drivers of what made today’s international system hang together. Our argument thereby furnishes a novel historical-sociological account of technologists as worldmakers, while contributing to IR’s burgeoning interest in infrastructural politics.