The three-dimensional folding of chromosomes is essential for nuclear functions such as DNA replication and gene regulation. The emergence of chromatin architecture is thus an important process during embryogenesis. To shed light on the molecular and kinetic underpinnings of chromatin architecture formation, we characterized biophysical properties of cohesin and CTCF binding to chromatin and their changes upon cofactor depletion using single-molecule imaging in live developing zebrafish embryos. We found that chromatin-bound fractions of both cohesin and CTCF increased significantly between the 1000-cell and shield stages, which we could explain through changes in both their association and dissociation rates. Moreover, increasing binding of cohesin restricted chromatin motion, potentially via loop extrusion, and showed distinct stage-dependent nuclear distribution. Polymer simulations with experimentally derived parameters recapitulated the experimentally observed gradual emergence of chromatin architecture. Our findings reveal molecular kinetics underlying chromatin architecture formation during zebrafish embryogenesis.