PSUs are one of the most common problem with systems.
Its not uncommon of to get a bad one.
They are also one of the easiest to test.
you dont even need to take your old one out of the case..
just unplug the current connectors, and plug the new ones in with the unit outside the case. There are plenty of grounds on the ATX connector.
Based on all the posts youve made, its not your cpu overheating (typically they throttle, and do not shut down the system) , or the GPU overheating (typically the driver does a thermal reset and does not shut down the system).
the PSU is the most logical choice at this point, until you rule it out.
IF you rule it out, id next look at your memory (timing setups in bios, and error testing)