Ok. I won't say its impossible but lets assume that our search engine is ready, programming and all is done, but the biggest question is how will you stop people to use Google,Bing, etc.
You know bing is better than google(It gives me better results while searching) but still bing is nowhere near google, why? Because people are addicted to google many doesn't know there are other search engines.
You have to do ads on TV, newspaper, on every other possible source just to catch people's eye and let them know there is other search engile also, and it will require around $xxx,xxx,xxx(estimate) just for advertising.
Also who knows if people will accept the new search engine besides google and they wont then congratz we've just wasted MILLIONS in nothing.
I'll tell you what google did, Internet was quite new google spot the opportunity and created SE as they knew, people will use their SE even if it wasn't good at all at that time because people had no choice, there were almost no alternatives.
for eg: A new product comes into market and there is very huge demand for that type of product but there are no competitors, so people will buy that product no matter what because they have no other choice.
I hope you get what I am saying lol.