A company can file for a H1-B before you start your job. I went through a similar situation last year. I graduated in mid June 2006 and my start date was in August. However, all my requirements were completed by early May. The company filed for H1B in late June (under 20,000 quotas for advance degree). To file for my H1B, among other things, I sent them a copy of my undergraduate degree and a letter stating that I have completed all my requirement from my graduate school (and I will graduate in June). So, for your case, maybe you can request for a letter from the registar's office stating that you have (will) completed all your requirements. Hope this helps.