This could have happened by the burial of organic matter. The decay of organic matter uses up oxygen, so if wastes were buried by high levels of sedimentation, oxygen could build up to critical levels.
This first animals with complete guts may have been key players in an increase of oxygen. They consumed organic material in the oceans and excreted fecal pellets which would fall to the ocean floor rapidly, instead of going through bacterial decay, which, again, would have consumed oxygen.
Image: detail of painting by Marvin Mattelson. National Geographic, October, 1993.