In normal individuals, oxygen-depleted blood from the right ventricle goes through the pulmonary artery to the lung to get oxygenated. The oxygen-rich blood goes to the left ventricle, from which it gets ejected to the aorta to the rest of the body.
In individuals with TGV, the oxygen-depleted blood from the right ventricle goes directly to the aorta to supply the rest of the body. This is not compatible with life, since the body would never get oxygen-rich blood. As a safety mechanism, an intracardiac shunt (ie: an atrial septal defect) opens, and this allows the oxygen-rich blood that returns from the lungs to partially mix with the blood in the right ventricle, allowing oxygen to be delivered to the organs of the body.
While the body does receive oxygen due to the intracardiac shunting, these individuals invariably have cyanosis.
While the x-ray may be normal at birth, the cardiac silhouette gradually enlarges into a characteristic globular or egg-on-its-side appearance.