Your problem will be finding a graphics card at all, let alone at anything less than 2x msrp.
You can probably find a i3-10100 processor, lga1200 motherboard and 16gb of ddr4 ram in the us for about $300.
Here is a review of the i3-10100 as a gaming processor:
https://www.techpowerup.com/review/intel-core-i3-10100/15.html
The graphics card is usually the important component for fast action gaming.
The i5-11400 processor is about $80 more and is a better long term gaming chip:
The Core i5-11400F coupled with a B560 motherboard make for an interesting build configuration, as it's significantly cheaper than the Core i5-11600K/Z590 and less than the cost...
www.techspot.com
In either case, consider paying a bit more for the non F processor which will include integrated graphics.
That can get you started if you have difficulty finding a reasonable graphics card.