Can a cheap A320 motherboard run XMP with a Ryzen 5 3600?

Probably, but you’ll have to set it manually. Most A320 boards got BIOS updates that let you tweak timings and voltage, so you can apply XMP settings by hand. 3200 MHz CL16 usually works fine; 3600 MHz is a toss-up. If your BIOS has an “Advanced” or “DRAM Configuration” menu, you’re good—if it’s locked down, you’re stuck at 2133 MHz.