First, try clearing the CMOS as UsandThem suggests - that is ALWAYS a good idea when you are having problems like this.
In this case, Gigabyte doesn't have a sticker on the MB/box label like some manufacturers do showing the BIOS initially installed and as you say there is no way to check since it won't boot. If the CMOS reset doesn't work, what to try next depends on whether you bought it new or used.
If you bought it new, and the box states it supports A-series APUs, then I'd presume that an A-series compatible BIOS (F32 or earlier) is installed and that the board is simply defective. I'd then return it if possible (preferred) or go through Gigabyte support for replacement (if no other choice). If you go through Gigabyte support, you might be able to request a board with the correct BIOS installed to support your CPU. Though, if you bought it through a retailer, they may be able to update the BIOS for you or even swap you with a board with a compatible BIOS for your APU. If you go this route, make sure not to install any BIOS above the F32 BIOS or you'll brick the board again (see the red BIOS notes on
this page).
If you bought it used, it gets far more complicated because the prior owner may have flashed the BIOS to F40 or higher for their CPU and thus prevented it from working with your APU. In order to test, you'd need a supported CPU on
this list that is not labeled as being a
Bristol Ridge CPU core to try to boot with. You could check with the place/person you bought it to see if they can test it for you to see if it will boot with a supported CPU. If you bought it from a person, they may know what BIOS is installed.
That being said, I don't see anything on the Gigabyte website that says you can't flash the BIOS back from F40+ to F32 (the last BIOS that supported Bristol Ridge APU/CPU cores). There are sometimes BIOS updates that can't be reverted, but none of those on the Gigabyte support site are actually flagged as being such. However, in the end it could be non-revertable and refuse to flash back to BIOS F32 - you just won't know until you try it.