Earth Kingdom Firebenders/Wan's People
The Earth Kingdom Firebenders (EFB) or "Wan's People" peoples were probably the ancestors of the dominant ethnic group in the Fire Nation we see today. My reason for believing they originally descend from Earth Kingdom People is as follows below.
The Fire Nation people we typically think of are predominantly based off of Japanese, Korean, and Chinese culture. In our history, Non-Ainu Japanese people are actually non-native. They descend from the Yayoi people, who came from China roughly 3500 years ago or so, displacing the native Ainu population. Something similar could have happened in the ATLA world, as we know that the Sun Warriors are a precursor civilisation (and probably native) to the Fire Nation.
Geographically this makes sense, as we see in the Era of Raava that the lion turtle they (Wan's people) live on lives in a tropical area, meaning it's somewhere in the Equator, and inside the Earth Kingdom. This is because we see Avatar Wan travelling across large swathes of land without crossing any oceans, so we can conclude that he was probably traversing the vast Earth Kingdom. Anyway, following the humans becoming independent and entering the world, these firebenders lived in the Earth Kingdom for a while before populating the Fire Nation Archipelago, and over millenia, slowly became the dominant ethnic and cultural group and displacing the Sun Warrior cultures.
As for their bending, the Sun Warriors probably got their bending independently.