Cortical signals have been shown to track acoustic and linguistic properties of continuous speech. This phenomenon has been measured in both children and adults, reflecting speech understanding by adults 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 may play a critical role in language acquisition. A recent investigation with infants Attaheri et al., 2022 [1] probed cortical tracking mechanisms at the ages of 4, 7 and 11 months as participants listened to sung speech. Results from temporal response function (TRF), phase-amplitude coupling (PAC) and dynamic theta-delta power (PSD) analyses indicated speech envelope tracking and stimulus-related power (PSD) for delta and theta neural signals. Furthermore, delta- and theta-driven PAC was found at all ages, with theta phases displaying stronger PAC with high-frequency amplitudes than delta. The present study tests whether these previous findings replicate in the second half of the full cohort of infants (N = 122) who were participating in this longitudinal study (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 cohort (122 infants recruited, 113 retained) using both infant-led and parent-estimated measures and multivariate and univariate analyses. Increased delta cortical tracking in the univariate analyses, increased ~2Hz PSD power and stronger theta-gamma PAC in both multivariate and univariate analyses were related to better language outcomes using both infant-led and parent-estimated measures. By contrast, increased ~4Hz PSD power in the multi-variate analyses, increased delta-beta PAC and a higher theta/delta power ratio in the multi-variate analyses were related to worse language outcomes. The data are interpreted within a “Temporal Sampling” framework for developmental language trajectories.