Is it probable that cyanobacteria were the first organisms to photosynthesize?

That depends on what mean by "cyanobacteria," and what kind of photosynthesis you have in mind. 
Photosynthesis is the conversion of light energy into chemical energy that an organism can use as fuel. There are two different kinds of photosynthesis -- oxygenic and anoxygenic. Oxygenic photosynthesis releases oxygen as a byproduct; anoxygenic photosynthesis does not.
There is widespread agreement among biologists that cyanobacteria were the first organisms to engage in oxygenic photosynthesis. However, the first photosynthesizing organisms ("phototrophs") may have been the ancestors of cyanobacteria.
Although biologists are still attempting to reconstruct this evolutionary history, the emerging consensus is that anoxygenic photosynthesis evolved first. In 2006, Armen Mulkidjanian and his colleagues conducted a genetic study of extant photosynthesizing bacteria species in order to reconstruct the likely evolution of photosynthesis. Their results led them to argue that the first photosynthesizing organisms were anoxygenic ancestors of cyanobacteria (see pnas.org link below). Later, these ancestral, photosynthesizing organisms gave rise to oxygenic cyanobacteria.
These events are thought to have taken place between about 3.5 and 2.5 billion years ago. After the emergence of oxygen-producing cyanobacteria, huge volumes of oxygen were pumped into the earth's atmosphere for the first time.
https://www.livescience.com/51720-photosynthesis.html

https://www.newscientist.com/article/mg19125654.200-revealing-the-dawn-of-photosynthesis/

https://www.pnas.org/content/103/35/13126.full