Well asking a prof to hire you is the conventional way but both ETH and EPFL, along with MPI (IMPRS programs) are moving to US style of admission cycle of once a year. Especially for AI related stuff. I'm not sure about how much the culture of open hiring from a prof will continue, until you graduate. So keep an eye on admission cycle in December and plan graduation accordingly. Even good profs in other Europe academia are being on onboarded to ELLIS (a Europe wide US style admission call for AI PhD programs). You would want to check that too! whenever you apply!