MAKIIVKA, Ukraine—A few miles from the frontvline of the brutal war in Ukraine, Olga Zaitsova, 31, turns to us in the back of the car to remind everyone that this mission is about precision and speed. The longer the evacuation takes, the higher the risk that the Russians will attack before we can liberate a badly injured 79-year-old man.
The Russian positions are only 900 yards from the village of Makiivka in the Luhansk region. The car drives along bumpy roads without much...