One of the great frontiers of consciousness science is understanding how early consciousness arises in the development of the human infant. The reciprocal relationship between the default mode network and frontoparietal networks—the dorsal attention and executive control network—is thought to facilitate integration of information across the brain and its availability for a wide set of conscious mental operations. It remains unknown whether the brain mechanism of conscious awareness is instantiated in infants from birth. To address this gap, we investigated the development of the default mode and fronto-parietal networks, and of their reciprocal relationship in neonates. To understand the effect of early neonate age on these networks, we also assessed neonates born prematurely, or before term equivalent age. We used the Developing Human Connectome Project, a unique Open Science dataset which provides a large sample of neonatal functional MRI data with high temporal and spatial resolution. Resting state functional MRI data for full-term neonates (N = 282, age 41.2 weeks ± 12 days), and preterm neonates scanned at term-equivalent age (N = 73, 40.9 weeks ± 14.5 days), or before term-equivalent age (N = 73, 34.6 weeks ± 13.4 days), were obtained from the Developing Human Connectome Project, and for a reference adult group (N = 176, 22–36 years), from the Human Connectome Project. For the first time, we show that the reciprocal relationship between the default mode and dorsal attention network was present at full-term birth or term-equivalent age. Although different from the adult networks, the default mode, dorsal attention, and executive control networks were present as distinct networks at full-term birth or term-equivalent age, but premature birth was associated with network disruption. By contrast, neonates before term-equivalent age showed dramatic underdevelopment of high-order networks. Only the dorsal attention network was present as a distinct network and the reciprocal network relationship was not yet formed. Our results suggest that, at full-term birth or by term-equivalent age, infants possess key features of the neural circuitry that enables integration of information across diverse sensory and high-order functional modules, giving rise to conscious awareness. Conversely, they suggest that this brain infrastructure is not present before infants reach term-equivalent age. These findings improve understanding of the ontogeny of high-order network dynamics that support conscious awareness, and of their disruption by premature birth.