Is the carotid artery the first vessel in the systemic circulatory system?

No, the carotid artery is not the first vessel in the systemic circulatory system. The first vessel is the aorta, which branches off from the heart's left ventricle and carries oxygenated blood to the rest of the body. The carotid arteries, which supply blood to the head and neck, branch off from the aortic arch.