In some mythologies, there is room for error. This is when the mythology has a set creation date, but also has a way to restart creation. In Hindu mythology, Shiva is known as the destroyer and creator. This allows for the mythological explanation of extinction level events like the meteor that wiped out the dinosaurs. By wiping the slate clean, new life was allowed to grow, without the hurdle of having to overcome any previous creation.
Universe from an Egg
There are many mythologies that have a creation story where the world and all that is in it came from a universal egg. This egg either is the start, or the being that laid it is the start of everything. What is shared in both is the presence of an egg that carries much of creation. There is not however a common myth of a universal chicken, so that answers that question.
Sole Creator
Other mythologies start with a sole entity that has existed since the beginning and sets the universe in motion. This does not mean that they always remain a sole creator as some also create other mythological beings that act as creators themselves. This can either form a hierarchal order to creation or take a more convoluted route.
Conceiving a Universe
Another common theme is a universe that is created from the joining of two beings, usually they are opposites or contemporaries. Some myths engender the two forces, while some label them as positive and/or light joining with negative and/or dark.
A staple in creation stories and in mythology in general is the personification of the natural forces. Both in Greek and in Egyptian mythology, The earth and sky are personified and are their own deities. In Greek Myth, Ouranos is the sky and Gaea is the earth, through their "joining" the titans are born who then appoint atlas to keep their mother and father apart. In Egyptian myth, Geb is the earth and Nut is the sky, And the children they had were Osirirs, Set, Isis, Horus, and Nephthys. By the command of Ra, Shu the wind god kept Geb and Nut apart.
In Both myths, the sky and earth are not only deities, but are in a relationship. They give birth to children and are then kept from one another. This shows that early civilizations saw the earth and sky as diametrically opposed forces. Both were needed to create life. Soil would be lifeless without water and light from the sky.