Not only is it possible, but it is becoming more and more likely to happen soon.
The reason it hasn’t happened yet is because nobody has applied the correct strategy yet. I do not think it would take heroic feats of execution, given the right strategy. In order to compete with Google’s strategy, or understand why it can be beaten in the first place, it is helpful to understand it:
Despite Google’s profits, talent, and maturity, the number of ways a user can possibly search for something is very limited. The way that Google Search presents results to the user, given an input query, is also out of the user’s hands. The user, no matter how savvy, cannot instruct Google to use a different kind of search algorithm. Nor can the user see the details of the algorithm that is chosen for them, as it is a highly guarded trade secret.
This is of course a deliberate choice on Google’s part. There are a few reasons, in my opinion, why Google’s strategy is successful: