Cheap PCIe powered GPU?

Okay, let me explain a bit. I have an HP PC with that propriety PSU, 4 pin to board, without any extra cords to power a GPU. Meaning it can only be powered by the PCIe.

Another issue is money is a bit tight but I don't mind running something a bit slow just to dip my foot in for more LLM and imaging. RAM is 32gb so that is fine and the CPU is a decent enough Intel Core i7-12700. But it has no GPU and the PSU is as I said HP.

So, does anyone have any ideas? I mean even a solid enough 6gb GPU would work as while it is likely slow for things I can at least start testing ideas and such out.

Or is the best option to find a new HP PSU that has an extra cord for a GPU? I looked and couldn't find one so would most likely need to take it in somewhere or buy from local small shop if very lucky. With PSUs it is the one real thing on a PC I want to be ne w instead of used.

Oh, and PSU is 310watts platinum I believe. So yeah, any help or ideas? Would greatly appreciate it.