Question about H1B application

USA_Newcomer

Registered Users (C)
I got a job offer that starts in late June. My company said it'll sponser my H1B visa. I graduate late May of 2006 with a Bachelor degree.

Since H1B application starts April 1st, will the cap be reached by late May ~ early July? The reason I ask is that I assume we can't submit our H1B application without a formal proof of my bachelor degree, which I probably won't receive until after my graduation in late May.

How should I go about this problem?
 
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