I was working on a startup and we were out of money. I applied for and found another job and let the founder know. On the Sunday before I was to start at the new place, we secured another round of funding, so the first thing I did on Monday was report to my new job and the second thing I did was resign from that job.

New boss was pissed, but it was the right call for me (and I couldn't have done it any earlier).

In your case, I'd give careful thought to the visa issue; I wouldn't sweat it on behalf of the major tech company at all. They've no doubt had worse behavior from candidates and they'll survive the loss. You probably won't be blackballed at that company, but do expect a question about it if you do decide to apply later.