I am not 100% sure what you are asking here. By the time a child is born, all of its organs are fully functional, and most have already been working for months. The birth process does force some changes in function, however. Before birth, babies get their oxygen indirectly, from their mother's blood stream; however, they practice breathing by drawing amniotic fluid in and out, which helps to develop the diaphragm and intercostal muscles. Once born, a baby must switch abruptly from breathing fluid to breathing air. This change also affects the heart, where an opening between the left and right ventricles must close soon after birth to make the blood circulate efficiently.
If you are wondering which organ works first during fetal development, the answer is the heart. Although it has not reached its final form yet, the human heart starts to beat just four weeks after conception.