The PC build you mentioned, consisting of the Ryzen 5 5600G, Gigabyte B550M DS3H motherboard, Gigabyte GTX 1660 Super graphics card, 2x8GB 3200MHz RAM, 128GB M.2 NVMe SSD, 500GB HDD, and FSP 650W 80+ Bronze power supply, is compatible and well-balanced. It should work together effectively to provide a capable gaming PC. Ensure to check for any specific compatibility requirements or BIOS updates for the motherboard before assembling the system.
My only suggestion is the processor. As you are gonna use a dedicated graphic card you do not need a integrated one along with the processor. Processors with integrated video are less powerful than the others. A model ending with 'X' is better.
Why not get the 5600X CPU (drop the integrated graphics version since you are buying a discrete video card) and a slightly larger M.2 NVME drive, like a 500 GB or even 1 TB? If you put games on the 500 GB HDD, that's going to slow you down in gaming. Can you swap out the 500 GB HDD for a 500 GB Sata SSD? Do you have two M.2 slots in that motherboard?
As Albert Einstein said, "I could have done so much more with a Big Al's Computer!".