Space systems are becoming an ever more important part of international security capabilities and practices. However, problematic interpretations of the Space Age are taking root in practitioner and academic circles along the contours of three sequential Space Ages. This article develops an original critique of these periodisations by applying a large technical systems approach and empirical research. It emphasises the role of space system builders and the prevalence of paradoxes in analysing space infrastructure as a method for critiquing three claims over the sweeping waves of democratisation, commercialisation, and militarisation in outer space that the periodisations make. This article proposes an alternative periodisation of a singular Global Space Age from 1957 that advances the counter-arguments that: first, power remains concentrated to a handful of space system builders rather than democratised to the many; second, that the space economy still relies on the state rather than being transferred to the private sector; and third, that the claims of sanctuary in space today ignore the spectre of space warfare that has long stalked space infrastructure. The infrastructural Global Space Age framing is offered as a useful materialist foundation for building bridges between international security, infrastructural technologies, and space security scholarship.