In the absence of any official explanation, here's my theory about the "head characters"/angels in Battlestar Galactica, including Starbuck. I think this explanation is internally consistent and explains just about everything that the creators of the show did not themselves explain about the subject.
The "angels" are a cylon projection at the individual level. Everyone can project them in the right circumstances because everyone has cylon mitochondrial DNA. When someone has prophetic visions, such as Joan of Arc, they're just tapping into the individual projection we're all capable of as descendants of Athena via Hera.
That same projection can happen more rarely at a collective level. Starbuck is one such projection at the level of the entire human race. She's not the only one, though. Every similar experience of divinity throughout human history is another example of collective cylon projection. Including the resurrection of Jesus Christ.
This ability to project at a collective level also enables the transmission of cultural, linguistic, and religious themes in general. It is effectively Joseph Campbell's notion of the collective unconscious. The reason gods have Greek names and that parts of the colonial culture are so familiar to us is that these ideas are held in common in the realm of projection.
This also explains why Hera is Mitochondrial Eve and why it was necessary for the cycle for the fleet survivors to appear when they did. The ability to project and pass on a collective human consciousness gave them a survival advantage. It did not exist in the primitive humans because it was a novel trait/mutation that did not appear until later in human history, possibly with the creation of the humanoid cylons. Without that trait the humans on Earth would likely have died out or never evolved into a civilization.
From there you can get into the typical arguments about time travel, but if we assume a single universe in a closed time loop this explains why "this has happened before and will happen again." Because for the cycle to be broken the fleet would have to fail to reach Earth, and if it didn't reach Earth, humans couldn't have evolved in the first place much less ever created cylons. The time paradox makes the final closing of the loop inevitable. In fact, cylon projection itself could be seen as a necessary mechanism by which time itself steers events toward the only possible conclusion. That makes the unseen first force time itself, manifested as god and angels. The divine purpose inherent in the universe, the meaning inherent in creation, is simply universal self-preservation.
This explanation is still "god did it," but it actually proposes a definition of what god is and a description of the mechanisms by which god's will is done.