If you don't have the necessary BIOS version that supports the latter gen processor, considering the board was released for the 12th Gen(prior to the 13th Gen), then yes the issue could be the BIOS version on the motherboard. Ofc, we're ruling out that you might've made a mistake while installing the processor onto the socket since bent or broken pins on the CPU's socket can also cause a similar issue.
Is there any way to update the BIOS without a BIOS flashback button or a supported CPU?
Sadly the motherboard manual, here
- page: 32+33, states that the board's BIOS will only be possible for update in one of two methods, none of which are associated with a BIOS FlashBack sort of scenario. You could source a CH341A BIOS Programming toolkit but I'd suggest a more sane approach, return the board and pick up a Z790 chipset platform or source a prior generation processor from your friend or neighbor or visit a local PC shop and see if they can flash the BIOS for you with a prior generation CPU dropped into it. I am ofc, assuming you didn't damage the pins on the socket, in which case a BIOS update isn't the root cause of your problem(perhaps).