The littlun with the birthmark probably died in the fire.

The smallest boys on the island are referred to as little ones, shortened to littluns.  There are many of them, and no one but Piggy ever seems to bother to get their names.  They live a pretty anonymous existence, taking a backseat to the larger boys.

When the littleun with the birthmark is first mentioned, he is a frightened little boy who does not want to speak before the group about the beast.

There was a group of little boys urging him forward and he did not want to go. He was a shrimp of a boy, about six years old, and one side of his face was blotted out by a mulberry-colored birthmark. (Ch. 2)

One day there is a huge fire, which gets out of control through the older boys’ carelessness.  The boys try to maintain a signal fire, but they did not intend to burn down the island.  It seems that the mulberry-faced boy might have died in the fire.

The death of this litteun is sort of a footnote for the older boys.  There is a description of how Henry, one of the bigger of the younger boys, is related to the mulberry-faced boy but doesn't seem to understand that he is gone.

He was also a distant relative of that other boy whose mulberry-marked face had not been seen since the evening of the great fire; but he was not old enough to understand this … (Ch. 4)

The boy is never seen again after the fire.  No one really asks any questions about him.  The older boys assume he died in the fire, and the younger ones seem to not understand that he is missing.  This is one of the first serious incidents in the book, and it shows how careless and callous the boys are about death.

The boy with the mulberry-colored birthmark on his face might have been the first to die, but he is not the last.  The deaths of Simon and Piggy can be more directly attributed to the descent into savagery of the tribe.  The littleun's death was an accident.  If he had not had such distinctive markings, they probably would not have noticed he was gone.

In the book Lord of the Flies, by William Golding, is there evidence as to what happened to the boy in the beginning with the mulberry colored birthmark?

In chapter two of The Lord of the Flies, the boys decide that they need to get organized to build a fire on top of the mountain to act as a signal. They hope that the smoke from the fire might be seen by a passing ship or plane and then lead to them being rescued.

As they start to build the fire, they get carried away and build a huge fire that quickly exhausts their store of ready fuel so they run off into the woods to find more wood for the fire. This disorganization is what likely leads to the loss of the kid with the mulberry colored birth mark.

It is when Piggy notices and points out the fire that spread down into the jungle that the boys also notice that the boy with the birthmark is missing. There is no physical evidence of his death, but only the fact that he is absent and no one knows his name. The huge fire stands out as the likely culprit in his death.