With strong data protection, copyright and privacy laws, it would be a nightmare for any company to train models because activists lawyers would sue left and right.
Even by some miracle they come up with the model, again the hardware would be from US companies. It would take years to build a European equivalent of AWS and not to mention the talent required to do that. Given how low the wages in European countries are compared to American counterparts, and also lack of incentives from the governments I truly cannot think of a way how EU can catch up to US or China. Although I would love to be proven wrong