So, that's not an FX system at all. It's got a fairly decent Ryzen CPU with 4/8 cores/threads, and that's plenty for any current game models. You are fine in this area.
Your RX 580 is pretty capable as well. Unless you are trying to game at a higher resolution than 1080p it should be perfectly fine, and even at 1440p it should be ok with some minor settings adjustments on a per game basis.
The only thing that jumps out at me immediately is the lack of an SSD and the use of only a HDD for the operating system. Get yourself a good SSD like the 850 EVO, Crucial MX300 or Sandisk Ultra II. 250GB is normally plenty.
Then you can clone your current OS installation to that drive, wipe the hard drive and use the hard drive for storage of large or seldom used files and gaming files. This would help give the whole system a much quicker feel.
The second thing you could do at some point would be to add more RAM. If you currently have two 4gb memory modules installed I'd highly recommend replacing them with two 8GB modules rather than adding two more 4gb modules as Ryzen (Much like early FX systems did) has some peculiar issues with memory (Upgrading to newer bios versions mostly fixes these issues) and especially when there are four modules installed rather than just two. A lot of systems, old and new, actually have these issues so the use of four modules rather than two is only generally a great idea if you absolutely have to, like when you need more RAM but already have the highest supported capacity modules installed and have to install more modules, rather than bigger modules, to get where you want to be. Either way is an option though.
I would also recommend that if you do upgrade the memory, you go with faster sticks, since the ones that came in that system are only the basic 2133mhz modules and Ryzen seems to really respond well to faster modules. Something like 3000 or 3200mhz would be nice in a 2 x8=16GB package.
Other than that, cooling can be addressed with a higher end cooler or additional case fans, but I wouldn't bother with this unless monitoring software shows that you are borderline or having thermal issues.