Without conscious awareness all those billions of years would be less than the blink of an eye in duration.
Maybe it’s not so much a question of whether we have a soul but rather who or what it is that has conscious awareness. IMO our sense of existence as an individual body is an illusion.
This illusion is demonstrated by the mental condition known as dissociative identity disorder (DID), previously known as multiple personality disorder, where various personalities might be exhibited by a single body. None of the personalities is the correct one—they are all equally illusional.
Also consider that the sense of self is heavily dependent on memory. Memory is notoriously unreliable and subject to going away.
You can lose your memory and still experience conscious awareness. In deep meditation yogis are unaware of their bodies and have no thoughts or memories. They are in a super conscious state.
I lean toward thinking that reality itself is conscious and that our bodies are nothing but robotic instruments.