The earth’s atmosphere is mostly nitrogen and oxygen. What process released most of the oxygen into Earth's at?

The answer is photosynthesis. The atmosphere of the Earth was anoxic about 4.6 BYA. The asteroid/comet events gave way to some of the Earth's water. The volcanic out-ging and eruptions produced many compounds in the atmosphere, including nitrogen, methane, carbon dioxide, sulfur dioxide, water vapor, and others, but NOT oxygen. In fact there was no free oxygen at that time, which means there wasn't an ozone layer yet either. And the idea that sunlight broke apart the carbon dioxide molecules doesn't work because this does not happen. The only way that the Earth got it's first form of oxygen in the water and air was from photosynthesis.