It can be done with some compromises. Linus Tech Tips had a video (can't find the link atm) for building a 1080p/60ish fps on low sub $200 pc.
I'm actually doing something similar for my daughter. Bought an old HP Z420 with 8gb ddr3 and a xeon for £50 plus an nvidia 1660 super for £100, £30ish for an ssd and it's a perfectly valid basic gaming machine.