People love to say that Google has "relatively poor" performance.
Relative to what? Google has better performance than any other search engine. It's relatively poor compared to the imaginary ideal search engine that gives you exactly the result you want for any query regardless of whether the information even exists or not.
I think your startup plan should not be: "Step one: Displace Google Search." Instead, you find the underserved niche, people who care about quality search results (maybe in a specific domain), and you address that. As you conquer the small market you expand.
Google really does seem to be frustratingly bad these days.
And we have add a variety of competing search-engines that still aren't as good. It isn't like the idea hasn't been tried. For example DuckDuckGo, or even Bing, but there have been half-dozen others too.
Obsessive programmers like myself really want a search engine that does better and helps us find the weird corners of the web.
Most people do not care. They can type a question into Google and get an answer, and that's all they're looking for.