Gap in status, for instance, H-1B and H-4 status issues

I was on F1, and my spouse was on F2. My H1B was approved in 2020 for client A, but COS from F1 to H1B was denied, so I just continued my F1 status. Later, I moved to client B, and my employer filed an H1B Amendment and got the complete approval with I-94, effective 29th April 2022. After approval, we filed I539 for my spouse's COS from F2 to H4 (still pending) with a receipt date of 17th May 2022.

Question: Since there is a gap between my H1B start date (04/29) and my H4 receipt date (05/17), may the USCIS deny our case? If so, what are our best options to proceed further?