Both microbes and multicellular organisms actively regulate their cell fate determination to cope with changing environments or to ensure proper development. Here, we use synthetic biology approaches to engineer bistable gene networks to demonstrate that stochastic and permanent cell fate determination can be achieved through initializing gene regulatory networks (GRNs) at the boundary between dynamic attractors. We realize this experimentally by linking a synthetic GRN to a natural output of galactose metabolism regulation in yeast. Combining mathematical modeling and flow cytometry, we show that our engineered systems are bistable and that inherent gene expression stochasticity does not induce spontaneous state transitioning at steady state. Mathematical analysis predicts that stochastic cell fate determination in this case can only be realized when gene expression fluctuation occurs on or near attractor basin boundaries (the points of instability). Guided by numerical simulations, experiments are designed and performed with quantitatively diverse gene networks to test model predictions, which are verified by both flow cytometry and single-cell microscopy. By interfacing rationally designed synthetic GRNs with background gene regulation mechanisms, this work investigates intricate properties of networks that illuminate possible regulatory mechanisms for cell differentiation and development that can be initiated from points of instability.