Tbh in all likelihood it should be supported, however worth confirming if possible as every now and again VGA BIOSs change which can cause problems with older boards, someone may know more than me about the specifics, but it appears
@SkeeterUK is running an RX 6700 with an even older CPU without issue!
OK, so to upgrade your BIOS you'd need to get the correct BIOS file from the manufacturer's website. In your case we'll need to confirm the specific revision of your motherboard, as it seems there have been more than one. There are lots of software tools that can give you this information, one of them is
CPU-Z (assuming you don't have the box/manual and can't see it written on the board - usually underneath one of the slots.)
Once you've downloaded that (manufactuer branding is not important and I'm almost certain you'll be on x64 if running win7/10/11), run the program and go to the mainboard tab. It should hopefully list the revision there as well as the current BIOS version.
Rev 1.0 BIOS page is here:
https://www.gigabyte.com/Motherboard/GA-Z97X-SLI-rev-10/support#support-dl-bios
Rev 1.1:
https://www.gigabyte.com/Motherboard/GA-Z97X-SLI-rev-11/support#support-dl-bios
Rev 1.2:
https://www.gigabyte.com/Motherboard/GA-Z97X-SLI-rev-12/support#support-dl-bios
however the latest download for any of the revisions is from 2016 (i.e. before the RX6600 came out)
Once you have the correct BIOS, you will need to copy the file to an appropriately sized (ideally 1-2GB or less) and formatted (Fat32) USB stick, then boot in to the BIOS menu (usually done by spamming the DEL key on boot), there should be a menu option to flash BIOS.
Once you've run that your PC should either restart itself (could be several times) or confirm that flashing is complete, after which it should boot in to the new BIOS successfully.
There will also be plenty of youtube vids showing the process, albeit for other models of board, but the steps should be the same