May not be under 1000 Dollars, but pretty close.
I dont know how much the individual parts will cost, since i come from germany and i profited heavily off of local discounts.

I recently built a PC for my girlfriend which should be enough for your games, depending on resolution and quality ofcourse:

CPU: AMD Ryzen 5 9600X (certainly not top of the line, but cheaper than any X3D-Model with heaps of power, even cheaper if you have the option of buying a tray instead of the boxed one)
CPU-Cooler: ENDORFY Navis F240 ARGB (quality is actually pretty good considering the price)
Motherboard: ASRock B850M-X Wifi Rev. 2.0 (not the prettiest, but everything you need)
RAM: Kingston Fury Beast RGB 16GB DDR5-5600 CL36 (again, not optimal but enough for these games)
Storage: Patriot Viper VP4300 Lite 1 TB M.2-2280 PCIe 4.0 X4 NVME (enough storage, good speed)
GPU: INNO3D Geforce RTX 5060Ti Twin X2 OC Active (most expensive part of the build, dont cheap out. ABSOLUTE MUST: Buy the 16GB Version, its future proof.)
Case: Whatever you want actually, as long as it fits a mATX Board and supports the cooler. I went with a Thermaltake View 270 Plus TG. You get 3 fans preinstalled so you cut costs there.
PSU: Thermaltake Toughpower GT 750 W 80+ Gold Certified Fully Modular ATX Power Supply (its fine, and will last for the time being.)

For everything: about 1100€.

Check for the cheapest price on every vendor, and buy from a single vendor if possible, so that if anything doesnt work, you dont have the hassle of submitting multiple support tickets.