There’s no science of the soul, and probably no such thing as a “soul”.
There are scientific studies of consciousness which look at “neural correlates of consciousness”, and some philosophical topics pertaining to the nature and ontology of consciousness.
There’s philosophy of mind.
There’s philosophy of space and time.
There’s philosophy of self.
We experience a ‘flow of time’ in seemingly continuous self-awareness, with our ‘self’ existing on a continuum of time from our earliest memories to death. This apparent continuity of consciousness and the self is perhaps what motivates ideas about the ‘soul’.
My own view is that the flow of time, the continuity of consciousness and the sense of self are all illusory. Ontologically, consciousness is a moment to moment reconstruction: like being annihiliated and recreated billions of times a second.