Run dxdiag to find out if you have DX12 installed
Run Windows Update to make sure you have all current updates.
The minimum specs for Apex call for 2GB VRAM so you may have trouble with your current video card.
Runtime Support <> Native DX12 support although I cannot confirm/deny the use of a GTX580 in Apex.
Your CPU MIGHT be an issue indeed; as I noticed in another thread, the 2-series is almost 4 years “too old” compared to the 4-series that is listed as needed.
That said, a friend on another forum is running a 2600K (without integrated graphics) together with a GTX980 and it works. Well, with works, I mean the CPU gets hammered with I/O while the GPU is overpowered so the best he can do with Apex is something like 1600x900.
358.70 beta driver enables dx12 on Fermi cards, so will let you download and install apex. However, Fermi doesn’t support resource binding tier 2, so it will error on launch. This is a hardware limitation of Fermi, so pretty much no hope on Fermi unless they modify the game to use resource binding tier 1 (unlikely imo).