Even though there is not an out-of-the-box option for modifying a no-results page, the InstantSearch Results Page is quite customisable, even when there are no results returned.
Here are a few points of reference that should be helpful in your customisation:
- Handling No Results with InstantSearch hits 'empty' template.
- Customising the InstantSearch Results Page in Magento (this references the
hitswidget mentioned above) - How do I handle no results pages? (in addition to some of the information above, this guide also provides insight on how to avoid searches that return no results)
You can also implement Algolia's Query Suggestions feature and then enable the automatic population of suggestions on a "No Results" page by toggling the Show query suggestions when no results setting in the Magento Admin by navigating to Algolia Search > Instant Search Results Page
