Looks like your motherboard is missing the backplate. See those 4 holes in the motherboard one in each corner of your CPU socket. That is where your CPU Cooler is attached to the metal back plate.
Your Ryzen 5 3600 comes bundled with the AMD Wraith Stealth CPU Cooler:
Looking at your photo you seemed to have a MSI Carbon motherboard. I found one at MSI and it shows you are missing the CPU Cooler brackets that come with all motherboards:
Most likely when you removed the Wraith Stealth CPU Cooler the Motherboard's back-plate fell off leaving those 4 empty holes which is why you can't install your CPU Cooler.