Travel before h1b start date

I am currently on F-1 status, which expires on July 10. My H-1B petition has been approved with a start date of July 1. Due to visa appointment backlogs in India, it would be very difficult for me to travel after July 1, obtain an H-1B visa stamp, and return to the U.S. in a timely manner.

Given this situation, would it be safe for me to travel to India now and return to the U.S. on my valid F-1 status before June 30, prior to my H-1B status taking effect on July 1?