Realistically if I were trying to beat Google I wouldn't be building a search engine. What can you offer that they can't? And if you even begin to compete with them there, what steps can they take that you can't recover from?
Instead, I would focus on beating them first, building search later (if search is what you actually care about). What's Google's weakness? Figure out "the cord that makes them run" (to paraphrase Meredith Vickers in Prometheus) and relentlessly attack that (legally, of course, this is business not cartel turf war). I have no idea what that might be, but Rome fell, IBM fell (well, stumbled, I guess?), so Google must have its Visigoths or Bill Gateses or whatever.
You built something cool, that replicates the functionality (80%). Cool. Good for you. You proved you can do it. Now decide if you really are serious about "beating Google", and figure out an effective way to do that. Search engine is not the way.
Anyway, Google built the (past of) search. If you really wanna do search, build the (future of) search. I dunno, like AR/VR search? Search for FBs AR platform? I have no idea but text search on WebPages is the past. Google already won. Get over it and move on. Build the future, or go build a better steam engine, you know, for like fun and stuff. Because it's cool, but it won't ever beat Google. Sorryz Cliqz