I dont know US cable size standards..

But Yes solder 4 x 2.5mm cables to each live and neutral

Then solder all the 0.75mm cables into a neat solder join, add heat shrink, then join to the 2.5mm cables

I sometimes use electrical blocks rather than solder, but that gets messy.

I add a fly lead for power for fans etc (which is the 4th cable from the PSU)

You can even solder like a 2 x 6mm2 cable to the PSU then add a distribution block.