If you don't have a Visa, I probably would not move before you do - H-1B visas are a lottery and O1 visas takes up to a year to get before you can even start working. Yes companies do conduct online interviews and will try to get you a visa before you move but it is hard.
Another route could be working for a European consulting firm or a Swedish company with an office in SF, then move to the US via them. Good luck!
If you want a larger company, find some job postings and apply, though ideally you'd want to speak to someone at the company. And yes, online interviews are quite common.