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.
![Screenshot 2024-02-20 183152.png Screenshot 2024-02-20 183152.png](/t5/image/serverpage/image-id/105075i95E0B06FD8CEB3B4/image-size/large?v=v2&px=999)
Your Ryzen 5 3600 comes bundled with the AMD Wraith Stealth CPU Cooler:
![Screenshot 2024-02-20 182720.png Screenshot 2024-02-20 182720.png](/t5/image/serverpage/image-id/105073iB781E63562288194/image-size/large?v=v2&px=999)
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:
![Screenshot 2024-02-20 182720.png Screenshot 2024-02-20 182720.png](/t5/image/serverpage/image-id/105074i039DC14AD4A5660A/image-size/large?v=v2&px=999)
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.