Final answer:
An arterial blood gas (ABG) analysis is the first assessment after the initiation of mechanical ventilation, providing vital information about the patient's respiratory status.
Step-by-step explanation:
The first assessment after initiation of mechanical ventilation is an arterial blood gas (ABG) analysis. This test is critical because it provides immediate information about the levels of oxygen and carbon dioxide in the blood and the blood's pH, indicating how well the patient is being ventilated. Although chest X-rays, pulmonary function tests, and bronchoscopy are valuable tools in assessing pulmonary health and placement of the ventilator's endotracheal tube, they are not the first step following mechanical ventilation initiation.