According to the creation epic how did the present order of the universe come into being?

That really depends on which creation epic you are referring to. There are many.

In the Babylonian story, Marduk defeated Tiamat and created the world using her carcass.

Judaism and Christianity have a different story. According to the standard Christian Bible, this is how the present order of the universe came into being.

Our world and the heavens we can see were created in three days of the original six days of creation.

On the first day, light was created and day and night came into being.

On the second day, our skies were created.

After the third day's creation of seas, land, and vegetation, came the fourth day's creation of the sun, stars, and moon, to help us mark time.

Sea creatures and birds were created on the fifth day and on the six day, land animals and man were created. At the end of the sixth day is the comment that this was how the heavens and earth were created.