That " no results" is configurable, just like a form success message is.
Click on your Search Results Wrapper, and then under settings, choose No Results.
Put whatever you want there.
Another option is to use real results.
Search works with a querystring, so on entry to your search page, you can have a script check for that querystring and redirect if it’s missing.
e.g. if there is no querystring, you can redirect to /search?query=test and then you’ll see results, that will function as a default search.
A third option…
Don’t link to your /search page directly. There’s probably not much value to that.
Most of the time, you’d use the search widget on other pages, e.g. in your site footer-
This way, any time someone sees the search results page, it’s because they’ve actually requested a search.