I think eventually more people will realize that the modern web is terrible and they will get fed up with it. People are already building alternatives. There are several situations that could cause Google to lose a foothold as the search behemoth and drive consumers to find alternate ways to find products.
Possible catalysts include: regulation of search or advertising negatively affecting google, an unknown search competitor entering the market, another of the behemoths competing (amazon with search, bing getting their act together, etc.), antitrust suits, insert black swan event here.
I think the pendulum is also swinging towards smaller, local communities. Maybe that's just my bubble. Eventually everyone will get sick of it though, and something will change. I don't think we can predict what will replace it, but I hope it's not another big, centralized source. We've seen the negatives of that.
I don't know how to build it, but to me the ideal Google search killer would be:
1) Decentralized somehow. Hosting search indexes collectively in order to reduce the need for a single entity to host the data. Crypto has this possibility maybe. But I don't know how well it could be implemented, and whether you could have search still be "free" like Google is. How do you solve for that problem?
2) Filters out the SEO spam. Yes, this is a huge problem. My idea to fix it is manual curation. Not scalable. How do you solve that? I think something like StumbleUpon. A curated list of sites that is searchable in its own index. Perhaps there could be a trusted network of curated indexes. Members only to host the curated indexes to keep out the black hats, but free to search for the public at large.
I also think we need to educate everyday users to host their own sites on their own hardware. Making it super simple to spin up a web host in a VM that is running on a laptop in the bedroom. Or off a raspberry pi 0. Or whatever is cheap and available. Turn it off when you need to and the website goes offline. Yes, but that is okay in the interim to get Joe Regular hosting a website independently. Sure it's not okay for a business, but for your hobby site about bonsai trees, why not? Of course this is against most ISP's ToS so how do you solve for that? How do you give Joe Regular the ability to deploy a simple, secure website easily? How do you incentivize them to get out of the walled gardens? Give them a garden of their own.
That was what made the early web (as I knew it in the 90s and 00s) awesome. You were figuring it out on your own. Google/Bing/DuckDuckGo can stick around and be the digital yellow pages. They are good at that.
We need to build a new web for ourselves.