You should design the power-down and start-up circuit for the bandgap voltage reference at the same time.
Several types of Start-up circuits for CMOS BGR are for your choice.
1. Cap. based Start-up
Tha capacitor is initially zero which leads to the current generation in BGR loop and consequently, current mirror starts to charge the capacitor. Finally, the capacitor does not impact the main circuit any more.
2. Threshold of transistors
3. Partial current drops into PNP
Start up circuit provides partial current even after the BGR is normally triggered.