Build a gaming PC on a budget

I have my 12 year old son 100% of the time after a nasty divorce. The dude loves to game. Building an affordable gaming PC together would be amazing. I have been lurking here for a long time. I understand the cost of components increasing recently.

I’d like to build something with him that allows him to game online better than the all in one he currently has. But I want him to develop a passion for building a PC.

We are entry level. I don’t want to spend $3500 on the off the shelf set ups. Over a couple months I can afford over a thousand in the US and in dollars.

It’s more important to me that we learn how to assemble something together. Some anticipation of parts and putting it together is a good thing.

TL;DR: Father and son wish to build a gaming PC on a budget of a thousand dollars as a bonding experience that ultimately inspires the son to get into computers.