You could check the CPU compat list and see what better CPU you could use with that motherboard. Given that it's both a "locked" board and a budget choice you will likely have better results with a new mobo to support a higher TDP CPU. If you choose to go 3xxx you will likely want faster RAM as well.
It's probably not worth touching the CPU. At 4K, games will be almost entirely limited by graphics performance, and a faster CPU would do almost nothing for frame rates. A Ryzen 1600 should be pretty good for pushing 60fps in today's games, and higher resolutions are generally not going to increase demand on the CPU.
For 4K resolution, it's all about getting as much graphics performance as you possibly can. A GTX 1660 is a fine card for 1080p, but 4K works out to four times as many pixels that the graphics card needs to render, making it completely inadequate for running demanding titles at that resolution.
Unfortunately, as was pointed out, you currently need to spend a lot to get decent performance at 4K. The 2080 Ti, for example, would cost more than the rest of the components in this system combined. That card is also discontinued though, and Nvidia is expected to announce a new generation of high-end cards in the coming days. It's likely that level of performance will be coming to a somewhat lower price range, but I still wouldn't expect any of the new cards priced under $600 to handle 4K at max settings particularly well.
In my opinion, native 4K arguably still isn't worth aiming for at this time. The current "4K consoles" like the PS4 Pro and Xbox One X are not actually rendering most games at 4K, but rather upscaling them from lower resolutions, and typically running them at 30fps with the equivalent of medium-low graphics settings. We may see some games running at native 4K60 on the upcoming consoles, but upscaling and lower frame rates will likely continue to be common on those as well. And on the PC side of things, prices of the highest-end graphics cards tend to grow disproportionately to the amount of additional performance they provide, so the top-end models are not really practical for anyone who doesn't have money to burn. You're probably better off rendering games at a resolution like 1440p, and upscaling to 4K if desired.