Spatio-temporal fetal brain atlases are important for characterizing normative neurodevelopment and identifying congenital anomalies. However, existing atlas construction pipelines necessitate days for slice-to-volume reconstruction (SVR) to generate high-resolution 3D brain volumes and several additional days for iterative volume registration, thereby rendering atlas construction from large-scale cohorts prohibitively impractical. We address these limitations with INFANiTE, an Implicit Neural Representation (INR) framework for high-resolution Fetal brain spatio-temporal Atlas learNing from clinical Thick-slicE MRI scans, bypassing both the costly SVR and the iterative non-rigid registration steps entirely, thereby substantially accelerating atlas construction. Extensive experiments demonstrate that INFANiTE outperforms existing baselines in subject consistency, reference fidelity, intrinsic quality and biological plausibility, even under challenging sparse-data settings. Additionally, INFANiTE reduces the end-to-end processing time (i.e., from raw scans to the final atlas) from days to hours compared to the traditional 3D volume-based pipeline (e.g., SyGN), facilitating large-scale population-level fetal brain analysis. Our code is publicly available at: https://anonymous.4open.science/r/INFANiTE-5D74