Stem cells undergo cellular division during their differentiation to produce daughter cells with a new cellular identity. However, the epigenetic events and molecular mechanisms occurring between consecutive cell divisions have been insufficiently studied due to technical limitations. Here, using the FUCCI reporter we developed a cell-cycle synchronised human pluripotent stem cell (hPSC) differentiation system for uncovering epigenome and transcriptome dynamics during the first two divisions leading to definitive endoderm. We observed that transcription of key differentiation markers occurs before cell division, while chromatin accessibility analyses revealed the early inhibition of alternative cell fates. We found that Activator protein-1 members controlled by p38/MAPK signalling are necessary for inducing endoderm while blocking cell fate shifting toward mesoderm, and that enhancers are rapidly established and decommissioned between different cell divisions. Our study has practical biomedical utility for producing hPSC-derived patient-specific cell types since p38/MAPK induction increased the differentiation efficiency of insulin-producing pancreatic beta-cells.