Sir,
Sorry for late reply as I was traveling and this is not my primary mail ID. Got pretty excited reading the question you gave.

To go about building a search engine better than google first we must define what the search engine must do :

*It should take any query as input, make sense of it, then after going through its knowledge library/database, outputs the result according the query*

I strongly believe the solution to most problems is identifying the hidden abstracted pattern in data/information.

So we can initialy go with training a model to filter tons of raw meaningless data(that we get by 24/7 crawling the internet) under keywords.
After filtering and labeling the previously cluttered data we now have somewhat catagorized data( knowledge library/dictionary?).
All possioble words in dictionary will have some crawled data associated with it.

Now we are somewhat ready with our basic engine. If we search "man and the universe"
We get the intersection of the data under "man" and "universe" keywords in our library/dictionary and outputs it.

Next logical steps will be go about improving each part of engine like, adding natural language processing capablity to our query parser so we can now make sense of queries better and get more information out of it to search our knowledge library.
adding more types of filters and relations to our knowledge library and to organize the information in diffrent layers of abstraction.