A 3-day-old male neonate born to non-consanguineous parents presents with cyanosis (SpO₂ 75% on room air) and respiratory distress. Chest X-ray shows an 'egg on string' appearance with decreased pulmonary vascular markings. Echocardiography confirms transposition of the great arteries (TGA) with an intact ventricular septum. The neonate is currently on supplemental oxygen and prostaglandin E₁ (PGE₁) infusion. What is the most appropriate next step in management?