And mass market EVs weren't really a mass-market thing until Tesla pushed the luxury brands to compete with them.
Mass market EVs started appearing exactly after EU regulations forced them to be made.
Tesla has helped but be would have EVs today even if the company had never existed.
It's impossible to say what would have happened in a different timeline, but Tesla made electric cars cool. Yes, there were EVs before, they were half-assed token efforts by the big automakers to pretend that they were trying. Tesla forced them to be competitive.
Are you talking about the same EU regulators that barely gave volkswagen a slap in the wrist for dieselgate?
EU regulations had approximately zero impact on Tesla's formative years -- and Tesla was the first auto manufacturer to meaningfully commit long-term (and not lip service) to EVs. VW and others are still today talking about how they're playing catch-up.
Most governments e.g EU, UK, China all looking to curtail/ban ICE cars within the next few decades. And of course this has resulted in car manufacturers rapidly pushing EV cars.