The nature of the aegis depends on what source you're looking at.
Euripides suggests that the aegis was the skin of the slain Gorgon, but the Gorgon is commonly held to be a later addition.
Diodorus Siculus claims it was the skin of a monster that Athena killed and flayed.
The twelfth century Byzantine poet John Tzetzes claims it was the skin of the giant Pallas, who Athena slew.
But I think Hyginus has it right, that the aegis was originally a goat skin. This is because the word "aegis" (αἰγίς) means "goatskin". (My most knowledgeable Greek professor even related it to the golden fleece.)
The Autenrieth entry is also worth looking at because it relates it to a storm cloud, which is domain of Zeus, and may carry the implication that it is an inherent part of his nature, and was with him as soon as he could exercise power over the sky and related natural forces.
See Also: https://en.wikipedia.org/wiki/Aegis#Etymology