The vignette pairs two findings that, together, are almost diagnostic: jaundice that refuses to clear and a protruding umbilicus.
In congenital hypothyroidism, low thyroid hormone depresses uridine diphosphate glucuronyl transferase, so bilirubin conjugation lags and unconjugated jaundice lingers past the physiological window. The same hormone lack causes hypotonia and weak abdominal musculature, allowing an umbilical hernia to form. The full syndrome also includes a hoarse cry, macroglossia, constipation, a wide posterior fontanelle and feeding difficulty - remembered by the cretinism picture.
Diagnosis rests on a low $T_4$ with a high $TSH$; newborn screening detects it before irreversible neurodevelopmental delay sets in, and levothyroxine is started promptly.
Down syndrome is a distractor (it shares hernia/hypothyroid risk but not this specific dyad), cerebral palsy produces no jaundice, and biliary atresia gives conjugated jaundice with acholic stools.
\[\boxed{\text{Congenital hypothyroidism}}\]