Early stromatolites (once we can sort the biological from the non-biological accretions - not always easy) WERE Cyanobacteria. "Then plants evolved to soak up the CO2" sounds suspiciously like evolution having a plan... Cyanobacteria are photosynthetic, which means that they were "soaking up the CO2" hundreds of millions of years before eukaryotic plants evolved, things like marine and freshwater algae (to start with). In fact, Cyanobacteria were almost certainly responsible for the conversion of the atmosphere into an oxidising one, likely to have happened over 2.1 billion years ago. There is hardly any evidence at all that eukaryotic green plants, or indeed any eukaryotic organisms, were in existence up to that time, at least not to anything like the extent needed for them to have much influence on that "soaking up."