Most often, a 404 error appears in the search if the page that shows the search results has been deleted. Smart Search & Instant Search adds new page to the Storefront / Web Pages section in your store after you've installed the app.
To recreate page again, click the Force re-indexation button in the Dashboard tab. Once the indexation is complete, the search results page will be restored.
Note: Be careful not to delete it in the future.