Our second son was (initially, thankfully) stillborn after a complicated delivery, yet the medical team managed to revive him and immediately put him in hypothermia (to 34° C), surrounding his head with some apparel containing essentially ice. Fast forward the 5 most painful days of my life, doctors warmed him back very slowly. He is now 4, and showing completely "normal" (in the statistical sense of the term) development.
Indeed, brain damage is not immediate in case of oxygen loss. It happens in phases. I am no expert, but I understood that most damage happen not immediately, and happen even if oxygen has been restored. Slowing down the body through hypothermia, seems to avoid the brain to "collapse".
Discussing with the head of the department (for a mandatory "retrospective"), he explained me that this technique had been devised after seeing that people who drowned in very cold water could be revived with less "impact" on their capacities than others. He also explained me that the technique was not always successful, but was the only "treatment" that had shown actual improvement of recovery chances in this kind of cases.