We conducted a quantitative comparison of developing sea urchin embryos based on the analysis of five digital specimens obtained by automatic processing of in toto 3D+ time image data. These measurements served the reconstruction of a prototypical cell lineage tree able to predict the spatiotemporal cellular organisation of a normal sea urchin blastula. The reconstruction was achieved by designing and tuning a multi-level probabilistic model that reproduced embryo-level dynamics from a small number of statistical parameters characterising cell proliferation, cell surface area and cell volume evolution along the cell lineage. Our resulting artificial prototype was embedded in 3D space by biomechanical agent-based modelling and simulation, which allowed a systematic exploration and optimisation of free parameters to fit the experimental data and test biological hypotheses. The spherical monolayered blastula and the spatial arrangement of its different cell types appeared tightly constrained by cell stiffness, cell-adhesion parameters and blastocoel turgor pressure.