Zygotic genome activation (ZGA), the onset of transcription after initial quiescence, is a major developmental step in many species, which occurs after ten cell divisions in zebrafish embryos. How transcription factor (TF)-chromatin interactions evolve during early development to support ZGA is largely unknown. We establish single molecule tracking in live developing zebrafish embryos using reflected light-sheet microscopy to visualize two fluorescently labeled TF species, mEos2-TBP and mEos2-Sox19b. We further develop a data acquisition and analysis scheme to extract quantitative information on binding kinetics and bound fractions during fast cell cycles. The chromatin-bound fraction of both TFs increases during early development, as expected from a physical model of TF-chromatin interactions including a decreasing nuclear volume and increasing DNA accessibility. For Sox19b, data suggests the increase is mainly due to the shrinking nucleus. Our single molecule approach provides quantitative insight into changes of TF-chromatin associations during the developmental period embracing ZGA.