According to climate researcher James Kasting, when the earth first formed there might not have been any oxygen around. There would have been life, just no oxygen.
For example, take methanogens, the microbes that make methane. They only thrive when there's no oxygen around. That why they live in airless places like the stomachs of cows. And according to the theory, back when the earth was young and there was no oxygen around, methanogens ruled and the atmosphere was filled with methane.
Oxygen came on the scene about a billion years later. But without methane, oxygen-producing microbes might not have evolved as quickly as they did. See, methane is a powerful greenhouse gas, meaning that it could have helped keep the sun's rays trapped near the earth's surface. This was important, since billions of years ago the sun was weaker than it is today. So without the methane-induced greenhouse effect, the earth might have frozen solid until the sun got hotter.
The earth would have become way too hot, if not for the fact that the methane rich atmosphere could have helped to deflect enough incoming sunlight to maintain a delicate temperature balance. Maybe the earth stayed warm, but not too warm, until oxygen-producing microbes evolved and filled the atmosphere with oxygen, which drove away most of the methane.