Early developmental specification can be modeled by differentiating embryonic stem cells (ESCs) to embryoid bodies (EBs), a heterogeneous mixture of three germ layers. Here, we combine single-cell transcriptomics and genetic recording to characterize EB differentiation. We map transcriptional states along a time course and model cell fate trajectories and branchpoints as cells progress to distinct germ layers. To validate this inferential model, we propose an innovative inducible genetic recording technique that leverages recombination to generate cell-specific, timestamp barcodes in a narrow temporal window. We validate trajectory architecture and key branchpoints, including early specification of a primordial germ cell (PGC)-like lineage from preimplantation epiblast-like cells. We further identify a temporally defined role of DNA methylation in this PGC-epiblast decision. Our study provides a high-resolution lineage map for an organoid model of embryogenesis, insights into epigenetic determinants of fate specification, and a strategy for lineage mapping of rapid differentiation processes.