A 2-year-old child who has no recent history of illness suddenly appears cyanotic and cannot speak after playing with a small toy. You should:

In the scenario described, the child's sudden onset of cyanosis and inability to speak after playing with a small toy strongly suggests that the child is experiencing a form of airway obstruction, likely due to choking. When dealing with infants and young children who are choking, the abdominal thrust maneuver is the recommended action when the child is older than one year and is conscious but unable to cough effectively or breath.

By performing abdominal thrusts, you apply pressure to the abdomen in an upward motion, which can help dislodge the object causing the obstruction. This technique is particularly critical because the child's ability to communicate is compromised, and rapid intervention is crucial to restore their airway and prevent hypoxia.

The other options do not address the immediate need for airway clearance. Performing a blind finger sweep is not advised as it may push the object further down the airway instead of removing it. Simply giving oxygen and transporting the child does not treat the obstruction, as the airway remains compromised. Visualizing the child's airway without immediate intervention would delay necessary action to alleviate the obstruction.

Therefore, initiating the abdominal thrusts is the correct and most effective response in this emergency situation.