One more thing, regarding getting H1B or any other type of working visa, yes, you need to pass your exam first, then find someone to employ you, then get working visa (in your case H1B), then go to Social security office to get SSN, then get your license or PTLA status. The whole process can take a long time, I mean counting from after you pass the exam.
For example, after you pass your exam, it may take ???weeks/months to get a job. Right now job market is good so hopefully it won't take too long. But need sponsorship for working visa is another story. To get H1B on regular basis takes 6 months (15 business days if you expedite the service). For SSN they always say 6-8 weeks but I got mine in 2-3 weeks. Then you send your SSN to state borad to get PT license, which took me another 2 weeks.
The only difference for me is, I was on TN not H1B. It took me total of 2 months before I started working (after passing the exam).