Cyanobacteria are much older than regular plants. At some point they were absorbed and became the chloroplasts of modern plant cells. At first cyanobacteria could not tolerate oxygen themselves, and what was disposed as a waste product was oxidized with iron, forming the "banded iron formations", a modern iron ore source. So there wasn't enough free oxygen to accumulate in the atmosphere.

Free-range bacteria don't fill all the ocean area they inhabit. Once the oxygen sinks like iron were full, and they were concentrated in plant cells that could tolerate oxygen, the oxygen production grew by a large amount, and significant build up could happen,