Organ and tissue formation are complex three-dimensional processes involving cell division, growth, migration, and rearrangement, which all occur within physically constrained regions. However, analyzing such processes in three dimensions in vivo is challenging. Here, we focus on the (comparatively accessible) process of cellularization in the anterior pole of the early Drosophila embryo to explore how cells compete for space under geometric constraints. Using microfluidics combined with fluorescent microscopy, we extract quantitative information on the nuclei morphology and cell boundaries in three dimensions. We observe T1-like spatial transitions along the apical-basal axis of cells in the anterior region. Such transitions facilitate significant cellular rearrangements, allowing the cells to pack into the restricted volume. Cells near the tip have markedly increased nucleus elongation, suggestive of significant stress. Further, these cells appear to undergo a skew transition along their long axis relative to the embryo surface, with maximum skew on the ventral side. Overall, cell deformation (skew) and geometric rearrangements (T1-like spatial transitions) appear to play important roles in cell packing in the highly curved three-dimensional environment of the Drosophila embryo pole.