Access and injecting into front end query search bar within plugin

Is there a way to access to the front end search bar within a custom plugin in such a way that I can set the query within it and search it?
For example, based on what the user enters within the options panel or upon an onclick within the visualization, change the input in the front end query bar and activate the search button?

It appears the value is surfaced through the route.


You might be able to trigger the fetch event in the discover controller, or you could trigger the click by targeting the search button.