It will almost certainly need a bios update if you are buying that board new. Generally motherboard manufacturers stop manufacturing a generational chipset as soon as they begin manufacturing the next gen chipset. So that was on an earlier bios version with the F11 version that supports the 9th gen CPUs not coming until after the newer boards began production.
It's always possible that any unsold stock was updated before being shipped to vendors, but I would not COUNT on it.
The cheapest CPU you could get that would work would make the investment higher than simply buying a newer motherboard that supports it out of the box, likely, even if you were to find a used one for 75% of MSRP. I'd just buy a board that supports it out of the box PLUS I'd buy a board that support both overclocking AND higher memory speed, otherwise you might just as well not even by that K SKU processor.
That's not to critique your choice, it simply makes more sense to spend less money. I seriously, SERIOUSLY doubt you can get that motherboard AND a CPU that will work in it, for less than you could just get a board that would work with it out of the box.
You're looking at about a 40 dollar difference between doing this, and the board you had picked out. No way you are going to find a CPU that works in that motherboard for less than 40 bucks if the 9600k doesn't work.
PCPP seem to think it WILL work, without a bios update, but the motherboard product page specifically indicates bios version F11 is needed for support. Perhaps you can check first with the seller to verify what bios version it will have OR buy directly from Gigabyte. The only other alternative would be to have the bios updated at a shop or send it to Gigabyte for updating, IF in fact it is not already on the latest bios when you get it.