Is it possible to implement a Recommender System without having a ratings/previous purchases similar data?
In the complete absence of user feedback, you can still build a (non-personalized) recommender system based on the products' descriptive features, e.g. by employing some distance metric.
In your case, there are at least two behavioral signals: clicks and search terms. Both can be used to personalize recommendations. I would start with getting familiar with session-based recommendations, which take into account user's actions in the context of the current session, and refine the recommendations incrementally (a kNN algorithm would be a good starting point).