The phrase "the child filled out" implies that the child has completed a form or document with required information. There are several synonyms for this phrase, including "the child completed," "the child filled in," "the child supplied information," "the child answered questions," or "the child provided details." Additionally, we can use alternative verbs such as "filled up," "wrote down," "completed the form," or "filled out the required details." Depending on the context, we can always choose the appropriate synonym that fits the intended meaning of the sentence.