Requiring users to know what sites they want in advance somewhat defeats the purpose of a search engine, no?
Obviously failing first requests isn't ideal but for popular requests it quickly becomes insignificant. Wikipedia might (if they don't already) want to make a similar suggestion for users to contribute when finding a low content/missing page.
The first request can also be called asynchronously, and display a message to the user that it is 'processing....'.
If I search for a news event it's a news site.
If I search an error message, I know the result is going to likely be stackoverflow, github issues or the forum of the library.
etc.
I don't think this strategy will get you all the way there, but it could be combined with other ways of curating sites to crawl.