If you can swing it, an L1 to an EB-1C might be an approach. Of course, that means finding a US company in the EU. The L1 is a dual intent visa like the H1B, so both can transition to a green card.
1. Do they heavily penalize my application for not having a VISA? 2. If I do get the job, do they give me an office in the EU until I get a VISA to go to CA?