The sound a lamb or calf makes is a bleat. If you hear tiny bleats coming from your barn, you'll know the new baby goats were born at last.
Many animals might bleat, though a bleat is a slightly weak, high-pitched sound, which is why it's typically made by young animals. When baby animals bleat, their mothers naturally go to them to feed or comfort them. You might also describe a human's cry or whine as a bleat, if it's particularly pitiful. The word comes from a Germanic root, and it's imitative of the sound itself.