Techniques are described herein for selectively processing a user's utterances captured prior to and after an event that invokes an automated assistant to determine the user's intent and/or any parameters required for resolving the user's intent. In various implementations, respective measures of fitness for triggering responsive action by the automated assistant may be determined for pre-event and a post-event input streams. Based on the respective measures of fitness, one or both of the pre-event input stream or post-event input stream may be selected and used to cause the automated assistant to perform one or more responsive actions.