You'd have to look for something second hand tbh for that price for Intel Nvidia.
PCPartPicker Part List
CPU: Intel Core i3-12100F 3.3 GHz Quad-Core Processor ($92.98 @ Amazon)
Motherboard: ASRock H610M-HVS Micro ATX LGA1700 Motherboard ($79.98 @ Amazon)
Memory: GeIL Orion AMD Edition 16 GB (2 x 8 GB) DDR4-3000 CL16 Memory ($31.99 @ Newegg)
Storage: TEAMGROUP CX2 512 GB 2.5" Solid State Drive ($25.22 @ Amazon)
Video Card: ASRock Phantom Gaming D OC Radeon RX 6500 XT 4 GB Video Card ($139.99 @ Newegg)
Case: Phanteks Eclipse G300A (1 Fan) ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: Thermaltake Toughpower GX2 600 W 80+ Gold Certified ATX Power Supply ($59.99 @ Amazon)
Total: $470.14
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2023-12-15 03:07 EST-0500
This list is the cheapest possible right now, it will play older games fine. 10100F is $10 cheaper but the motherboard is more expensive then because they are not being made any more. PSU is as cheap as I will recommend if you want to be sure the system will last more than a couple of years. Everything else is basically the cheapest available on Partpicker apart from case, which again is worth the extra $10 when it comes to cooling and longevity.
PCPartPicker Part List
CPU: AMD Ryzen 5 5600G 3.9 GHz 6-Core Processor ($131.63 @ Amazon)
Motherboard: Gigabyte A520M S2H Micro ATX AM4 Motherboard ($69.98 @ Amazon)
Memory: GeIL Orion AMD Edition 16 GB (2 x 8 GB) DDR4-3000 CL16 Memory ($31.99 @ Newegg)
Storage: TEAMGROUP CX2 512 GB 2.5" Solid State Drive ($25.22 @ Amazon)
Case: Phanteks Eclipse G300A (1 Fan) ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: Thermaltake Toughpower GX2 600 W 80+ Gold Certified ATX Power Supply ($59.99 @ Amazon)
Total: $358.80
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2023-12-15 03:20 EST-0500
5600G review here
iGPU bang for your buck
www.tomshardware.com
This list using integrated graphics almost gets you there, but its obviously AMD. You can ignore the warning for incompatibility, it will work with a newer BIOS and if the motherboard happens to ship with a very old one installed it has Qflash, meaning you can update it without an installed CPU.
Youd need a copy of Windows as well, which is another 100, but you can download and install from Microsoft and use it without a license, it will just have some features disabled and bug you to buy a license.