I would say you’re safe to live in Europe once you reach year Two and you’re CVG/ORD/JFK based.
Now living in Europe can mean many things, we talking 30 min outside of Frankfurt or 5 hrs from anywhere?
Pre COVID we had pilots jumpseating on any of the Majors. I’ve done so myself on DL.
Otherwise jumpseat on company airplane from Germany. Life will be easier once the world is back to normal. For instance DL used to have like 3 flights a day AMS-ATL.
If you made ATL your gateway you’d be golden for the above mentioned bases.