**Core Concept**
In a premature infant presenting with grossly bloody stool, abdominal distention, and increasing oxygen requirements, the initial diagnostic step involves evaluating the lower gastrointestinal tract for any obstructions or anomalies that could be causing the hemorrhage. This requires a comprehensive assessment of the abdominal cavity.

**Why the Correct Answer is Right**
The abdominal series, including X-rays of the chest and abdomen, is the best initial diagnostic step in this case. It allows for the identification of any intestinal obstruction, such as a malrotation or volvulus, which is a common cause of GI hemorrhage in premature infants. The abdominal series can also help to rule out other causes of abdominal distention, such as a bowel atresia or a Meckel's diverticulum. Early diagnosis and treatment of these conditions are crucial to prevent further complications and improve the patient's outcome.

**Why Each Wrong Option is Incorrect**
**Option B:** Fiberoptic endoscopy is not the initial diagnostic step in this case, as it is an invasive procedure that requires sedation and is typically reserved for more definitive diagnosis and treatment.

**Option C:** The Apt test, also known as the Apt-Downey test, is used to differentiate between maternal and fetal blood in a newborn's stool. However, in this case, the presence of grossly bloody stool suggests a more serious underlying condition that requires immediate attention, and the Apt test is not the best initial diagnostic step.

**Option D:** Routine stool culture is not indicated as the initial diagnostic step in this case, as it may delay diagnosis and treatment of a potentially life-threatening condition.

**Clinical Pearl / High-Yield Fact**
In premature infants, a grossly bloody stool and abdominal distention are red flags for a possible intestinal obstruction or anomaly. A prompt abdominal series is essential to identify the underlying cause and prevent further complications.

**✓ Correct Answer: A. Abdominal series**