[Urgent! Help!] H1B approved followed by offer rescind before orientation

I entered USA via L2 visa. A research institute would like to employ me and filed application for change of status from L2 to H1B. I received approval email of H1B on Jun 23 (but I have not received the I797 approval notice). The research instate rescind my offer on Jul 2, just before my orientation on Jul 6.

My question is: Has my H1B status been started? If yes, what should I do? Do I need to change H1B back to L2 immediately?

Thanks

Is this for a new H1? In that case it’ll be valid only after October, so you should find a new employer by then. Also consult a lawyer because USCIS does not like employer changes before start of H1s

Thanks for your kindest answer. Yes, this is a new H1 with cap exempt.