Why would EU building it themselves going to happen? Either it could be profitable for company to operate in EU or it is not. Assuming current US companies are efficient enough and if they couldn't be profitable, why could be a same thing built by EU is profitable there. In fact it is opposite as they couldn't track as much as American companies even outside EU.
I don't think it can. Maybe they can buy yandex, but i think europe has drained its talent tothe US. And even if they build it, how will they monetize it?