The price of that system is unfortunately going to end up being a lot more than 4k, you'd need a CPU that has at least 64 lanes of PCIe. That's going to be either a Xeon W or a Threadripper CPU, with the motherboard RAM, etc you're probably looking at least another 2k.

Also kind of a nitpick, but I'd call that 8 GPU system, each BMG-G21 die has 20 Xe2 cores. Also even though it would be 4 PCIe cards it is probably best to think of it as 8 GPUs (that's how it will show up in stuff like pytorch), especially because their is no high-speed interconnect between the GPU dies colocated on the card. Also if you're going to do this make sure you get a motherboard with good PCIe bifurcation support.