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.

Your best bet is to watch for used ones for sale that fit your requirements. It’ll be very difficult to build a new PC for $100 without some used equipment.

Might be different where you live, here with used parts you could get a Ryzen 1700, mainboard, 16 GB RAM, and a RX 570 for about $170. Decent for somewhat recent games, decent upgradeability. You're still missing case, PSU and storage (new SSDs are really cheap though), and peripherals like monitor, keyboard and mouse, if you still need those as well. You can get a cheaper system on older platforms, but then you'll have to replace the whole CPU/mainboard/RAM combo to upgrade.

1. Google a bit for ideas on what you can do with an off-lease OptiPlex, just make sure to get one that is not small form factor (SFF), so that you can fit a GPU in there without having to get medieval on it.

https://www.popsci.com/story/diy/build-cheap-gaming-pc/

2. Look on Craigslist/Nextdoor/FBMarketplace for a beater of a laptop with a discrete GPU. I'm in CHI area and see options like T510 and E6430, each for right around a hundo, along with a few antique tower desktops.

3. If you are just itching to try some Stable Diffusion, consider if a virtual pc is good enough... You could scratch that itch right now for pocket change.

https://towardsdatascience.com/create-your-own-stable-diffusion-ui-on-aws-in-minutes-35480dfcde6a

Good luck on your quest!