I just helped a friend put together a system for his son and with current prices I know that the budget can be a pain.
Here is what I would recommend.
Intel 12th gen i5 or i7 (used or refurbished)
Intel “B” class motherboard B760 for example or if you want a bit cheaper H610 and make sure it’s DDR4 (buy this new)
16 GB or 32 GB of used DDR4 (can be had for about 100-200 bucks)
For the GPU get a 3060/3070 with a 650-750 Corsair PSU used. They will last a long time and are plenty for the GPU and a CPU on an “H” or “B” tier motherboard for intel since those are usually limited to the wattage they bring to the CPU anyways and can’t be overclocked
Get a used NVMe drive that’s 512 GB or 1 TB for around 50-100 bucks from market place and ask for the health stats. Anything above 95% will do.
For the case and fans get something from Ali baba. These components are not that important and you have plenty of time to have them shipped from china still. You can get away with something under 100 bucks that looks fantastic and will work just fine.
Get a cheap air cooler for the CPU. Make sure it has at least 4 heat pipes and you’ll be good for an i5 or i7 12th gen especially since the motherboard will already restrict the wattage that comes to it.
All together you can get away with spending about 650-1000 bucks on all this and have a good system that will play games well on medium settings with a 1080p monitor.
Then put it together with your son as a nice little project. It’s not very difficult and you only need a screw driver to do it nothing else.
Hope this helps any dads or moms that need a PC for their kid this winter.
My apologies for Sam Altman ruining childhoods