Entry Date

My daughter is going for emergency surgery, not able to fly back to US. She lives in Wuhan China. My US passport has not arrived yet but am getting it expedited - did not expect to travel till April when her baby is born. Both the baby and mother are in danger. In filing for my wife's China VISA, she already has her passport and is looking to leave before me, the application requires a date of entry. The date is dependent on how quickly we receive her VISA. Can I put on the application a hopeful date of date and then, if needed, she can fly out a few days later? Is their faster service on VISA than the expedited 3 days?