首先，即使h1b申请加急，也只是加快批准速度。而h1b的生效日期仍旧是10月1号。没办法提前。
不过别担心，你的情况符合Cap-Gap Extension:
A cap-gap extension is a regulatory provision which extends an eligible F-1 student's status to bridge the gap between the end of F-1 status and start of H-1B status, thereby allowing the student to remain in the US during the "gap." The cap-gap extension is available to students who, as of April 1st (the beginning of each fiscal year) were either on approved OPT or in their 60-day grace period and have a pending or approved change of status H-1B petition with the USCIS that was filed prior to the expiration of their OPT or 60-day grace period. Those filing for H1-B via consular processing do not qualify for the Cap-Gap Extension.
If the employer filed your H-1B (change-of-status) petition and it is received by USCIS prior to your post-completion OPT expiration date, you qualify for an extension of your OPT employment authorization.
If the employer filed your H-1B (change-of-status) petition and it is received by USCIS after your post-completion OPT expires but during your 60 day grace period following OPT, your F-1 status and permission to remain in the US are extended but you are not eligible to work.
