IMHO it's basically impossible to build such a PC. The small size plus high thermal load of a modern GPU means it cannot be cooled quietly. Intel's line of NUCs had some gaming models back in the day (e.g. Skull Canyon), but the graphics were the Intel midrange GPU and they had tiny noisy fans. Anything approaching Nvidia 4070 or 5070 series and you've got up to 300 more watts TBP heating up the system on top of the CPU etc.
My last small form factor gaming PC was an Origin Chronos. It was great but it was definitely not quiet. The larger Origins offer liquid cooling but I'm guessing it can't be done in that small form factor.
The new APU from AMD can makes it come true. Its iGPU is on par with rtx4060 laptop, which is far from 4070 desktop, but should be enough for 1080p gaming and light 2k gaming.
My last small form factor gaming PC was an Origin Chronos. It was great but it was definitely not quiet. The larger Origins offer liquid cooling but I'm guessing it can't be done in that small form factor.