This answer is, of course, no. Adam did not have an umbilical cord. He was made of dust directly by God. This is not so trivial as it may sound. The first human was made of dust.
Eve, also was not born, but made from Adam. Today we would call it cloning. But she was one step away from dust, and had no parents.
A Bible search of dust is very revealing. It starts In Genesis and is repeated in the resurrection from dust of Daniel 12:2. An attempt is made to deny this. Moderns do not acknowledge this sobering fact--we are all of dust, and except for those in the rapture, will return to dust.
There is no immortal soul in the Bible. Hell had not been invented yet. But for this grim condition, there is a wonderful remedy. Job knew about it. It is known as resurrection.
Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live: John 11:25