Cortical signals have been shown to track acoustic and linguistic properties of continual speech. This phenomenon has been measured across the lifespan, reflecting speech understanding as well as cognitive functions such as attention and prediction. Furthermore, atypical low-frequency cortical tracking of speech is found in children with phonological difficulties (developmental dyslexia). Accordingly, low-frequency cortical signals, especially in the delta and theta ranges, may play a critical role in language acquisition. A recent investigation Attaheri et al., 2022 (1) probed cortical tracking mechanisms in infants aged 4, 7 and 11 months as they listened to sung speech. Results from temporal response functions (TRF), phase-amplitude coupling (PAC) and dynamic theta-delta power (PSD) analyses indicated speech envelope tracking and stimulus related power (PSD) via the delta & theta neural signals. Furthermore, delta and theta driven PAC was found at all ages with gamma amplitudes displaying a stronger PAC to low frequency phases than beta. The present study tests whether those previous findings replicate in the second half of the same cohort (first half: N=61, (1); second half: N=61). In addition to demonstrating good replication, we investigate whether cortical tracking in the first year of life predicts later language acquisition for the full infant cohort (122 infants recruited, 113, retained). Increased delta cortical tracking and theta-gamma PAC were related to better language outcomes using both infant-led and parent-estimated measures. By contrast, increased ~4Hz PSD power and a greater theta/delta power ratio related to decreased parent-estimated language outcomes. The data are interpreted within a "Temporal Sampling" framework for developmental language trajectories.