Self build won't be much cheaper to be honest, a lot of places have discounts on prebuilds with older or excess stock. Especially on a low budget.
You definitely need a good graphics card. Apex will run on a 3400G in that CCL computer but only at 720p low settings for 60fps, I doubt anyone wants to be doing that with a brand new PC, especially a streaming pc, game will look awful.
But again as I said streaming also requires a good processor rather than a low-end budget one. Apex is OK for low-end CPUs, but not so much when streaming is thrown in too. The 3400G is ok for both on games like that.
The ideal combo is something like ryzen 2600 + rx570/rx580, game would run at ultra and stream well. If you can't afford that, I would build a ryzen 2600 base and then buy a cheap 2nd hand graphics card to get you through for now. 8gb ram is fine for now for that and can be upgraded later.
Also you could consider 2nd hand. Some pcs on adverts are way overpriced but some might be open to good offers. I see a few RX570 PC's with OK processors that would likely sell for 350-400 if offered