**Core Concept**
The question is testing the knowledge of a congenital condition that affects the normal swallowing mechanism in newborn babies, leading to regurgitation of feeds and drooling of saliva.

**Why the Correct Answer is Right**
The most likely diagnosis is a congenital esophageal atresia with tracheoesophageal fistula (TEF). In this condition, the esophagus is not properly connected to the stomach, and there is an abnormal connection between the esophagus and the trachea. This leads to regurgitation of feeds and drooling of saliva. The condition is often associated with polyhydramnios during pregnancy due to the fetus's inability to swallow amniotic fluid.

**Why Each Wrong Option is Incorrect**
**Option A:** Congenital pyloric stenosis typically presents with projectile vomiting after feeding, not regurgitation of feeds and drooling of saliva.
**Option B:** Gastroesophageal reflux disease (GERD) can cause regurgitation of feeds, but it is not typically associated with continuous drooling of saliva in newborns.
**Option C:** Esophageal atresia without TEF would still cause regurgitation of feeds, but it would not lead to drooling of saliva.

**Clinical Pearl / High-Yield Fact**
Congenital esophageal atresia with TEF is a life-threatening condition that requires prompt surgical intervention. The "three-pass sign" is a classic clinical sign, where the baby passes three objects through the mouth and then regurgitates them, indicating the presence of a tracheoesophageal fistula.

**Correct Answer:** C. Esophageal atresia with tracheoesophageal fistula.