Developmental psychology focuses on how psychological constructs change with age. In cognitive development research, however, the specifics of this emergence is often underspecified. Researchers often provisionally assume linear growth by including chronological age as a predictor in regression models. In this work, we aim to evaluate this assumption by examining the functional form of age trajectories across 25 phenomena in early linguistic and cognitive development by combining the results of multiple meta-analyses in Metalab, an open database. Surprisingly, for most meta-analyses, the effect size for the phenomenon did not change meaningfully across age. We investigated four possible hypotheses explaining this pattern: (1) age-related selection bias against younger infants; (2) methodological adaptation for older infants; (3) change in only a subset of conditions; and (4) positive growth only after infancy. None of these explained the lack of age-related growth in most datasets. Our work challenges the assumption of linear growth in early cognitive development and suggests the importance of uniform measurement across children of different ages.