Plato, in the Timaeus, argued that although the physical elements might be eternal, the cosmos as their current arrangement is not.
Since the cosmos is not eternal, it follows that it somehow came into being. Everything that “becomes” must have a cause, something or someone ordering it into being. This is an early concept of god, though not yet the omnipotent creator of later monotheism.
The Greeks believed in the soul, and their picture of the soul was much broader than ours. For instance, the world itself was sometimes seen as a living, spiritual being. Another important difference is that the Greeks did not try to locate the soul, which was assumed to be more or less evenly distributed throughout the body.
These arguments are known as causal arguments because they boil down to our innate desire to reduce everything to causes and effects. If something moves, we assume there must be a mover.
This line of thinking has profound moral implications. If there is a god, and god is good, and god does good, then god made us, and we must be good. Plato was deeply critical of atheism, there is little room for non-believers in The Republic.
Plato thought that if you make moral progress in this life, you will have a better start in the next life. The soul, for Plato, is a simple rather than a composite thing. To be simple means to be an indivisible unit, like god. What is immaterial is un-choppable (indivisible). What is indivisible is indestructible. For Plato, what is immaterial is indivisible.
The soul activates bodily potential, it is the source of life. Lives end, but souls are endless. Not all souls are rational. Human souls are, but the souls of flies are not. Aristotle later recognized three kinds of souls (nutritive, sensitive, and rational), but that is beyond our scope.