Chaos as the primordial state
The Enuma Elish offers a cosmology in which matter has always existed. What separates this reality from the primordial reality is not matter, but orchestration and order. This theme is primarily explored through the slaying of the beast who represents the oceanic waters.
In Sumerian cosmology, the ocean waters are the image for chaos and formlessness. When Tiamat ruled over the divine realm with Abzu (also waters), there was no discernible nature, but when Marduk kills Tiamat, immediately, reality reflects its new management, setting the stage for the heavens and the earth. This theme is also hinted at in the Hebrew texts, and in fact, it comes up in almost all near-eastern mythologies.
The heavens are a kingdom
The Sumerian cosmology offered in the Enuma Elish also shows a divine government with one patriarch on the throne at all times. The nature of divine contest in the heavens is a competition for the throne so they have the authority to create.
Natural forces have supernatural causes
As a religious text, many historians and critics have suggested that these myths originated from a desire to explain the fascinating reality we live in. In the absense of religious doctrine, the early humans might have invented stories to explain to each new generation why things are the way they are.
Or maybe one of the myths is true, or something similar to it, and there was an era of human existence where the lines between the natural and supernatural were blurred. Regardless, the result is that the Enuma Elish attempts to explain why the natural forces exist, and they credit those to the forces of deities and their position in the kingdom of the gods.
The gods are not unchanging
The Enuma Elish seems to suggest that changes can happen in the supernatural realm that directly affect the realm of the humans. This led to the Sumerian religion being one of consistent devotion and practice, because the gods are not unchanging, so it's important to stay on their good side and remember the legends.
Life has an order
What this means is not that 'things happen for a reason,' but rather that the Sumerian cosmology as presented in the Enuma Elish shows a reality that has different strata. These levels start at the top in the realm of the divine ones, and then descend through the realms of titans and angels, to the second heaven, which is the sky and stars, and then to the land of the living and the air we breathe, and then lower through the animals according to their place on the chain of being, and then lower to the realms of death. This is common in the part of the world where the Babylonian empire was.
