Adaptive radiations have played a major role in generating modern and deep-time biodiversity. The Triassic radiation of the Archosauromorpha was one of the most spectacular vertebrate radiations, giving rise to many highly ecomorphologically varied lineages—including the dinosaurs, pterosaurs, and stem-crocodylians—that dominated the larger-bodied land fauna for the following 150 Ma, and ultimately gave rise to today’s > 10,000 species of birds and crocodylians. This radiation provides an outstanding testbed for hypotheses relating to adaptive radiations more broadly. Recent studies have started to characterize the tempo and mode of the archosauromorph early adaptive radiation, indicating very high initial rates of evolution, non-competitive niche-filling processes, and previously unrecognized morphological disparity even among non-crown taxa. However, these analyses rested primarily either on discrete characters or on geometric morphometrics of the cranium only, or even failed to fully include phylogenetic information. Here we expand previous 2D geometric morphometric cranial datasets to include new taxa and reconstructions, and create an analogous dataset of the pelvis, thereby allowing comparison of anatomical regions and the transition from “sprawling” to “upright” posture to be examined. We estimated morphological disparity and evolutionary rates through time. All sampled clades showed a delayed disparity peak for sum of variances and average nearest neighbor distances in both the cranium and pelvis, with disparity likely not saturated by the end of the studied time span (Late Jurassic); this contrasts with smaller radiations, but lends weight to similar results for large, ecomorphologically-varied groups. We find lower variations in pelvic than cranial disparity among Triassic-Jurassic archosaurs, which may be related to greater morphofunctional constraints on the pelvis. Contrasting with some previous work, but also confirming some previous findings during adaptive radiations, we find relatively widespread evidence of correlation between sampled diversity and disparity, especially at the largest phylogenetic scales and using average displacement rather than sum of variances as disparity metric; this also demonstrates the importance of comparing disparity metrics, and the importance of phylogenetic scale. Stem and crown archosauromorphs show a morphological diversification of both the cranium and pelvis with higher initial rates (Permian–Middle Triassic and at the base of major clades) followed by lower rates once diversification into niches has occurred (Late Triassic–Jurassic), indicating an “early burst” pattern sensu lato. Our results provide a more detailed and comprehensive picture of the early archosauromorph radiation and have significant bearing on the understanding of deep-time adaptive radiations more broadly, indicating widespread patterns of delayed disparity peaks, initial correlation of diversity and disparity, and evolutionary early bursts.