Maybe God had a belly button, that didn't come from being born. Maybe He just had one, for the same reason that He had a beard and fingernails - He just did. So, he made Adam and Eve in his image, and He made Adam's and Eve's belly buttons from scratch. Then, He decided that the simplest way of making belly buttons was to make them remnants of the umbilical cord, and He designed the umbilical cord so that it would, after it no longer bound mother and child, put in the final detail that made man in His image. If He hadn't had a belly button, then we wouldn't have anything left of the umbilical cord - God would've set it up so it would heal smoothly.