Based on the information from the wiki it seems that wild cards are purely random and that any egg can be a wild card. This could imply that the decision is made upon hatching; on the other hand an argument could be made that it is decided upon creation based on the fact that if one parent is a wild card then the egg has a higher probability of being a wild card.
One way to test this would be to save the game prior to an egg hatching. Then reset the game after the egg hatches and see if you have a consistent result. If you do then the egg is probably determined upon creation, if not, it's determined upon hatching.