If power consumption exceeds some rail's expected value it will do what you described (the power supply itself will do this...and it isn't just too much power being drawn, it's anything making the power unstable...switching supplies won't regulate if the consumption is too low so there is a fraction of a second after a power button is hit before the supply actually powers up...it is waiting for one of the rails to become stable).
The other time when it will do this is what is called a triple machine exception...this only occurs when there are seriously wrong software interrupt states in the kernel where data corruption is likely if continuing...the CPU will simply power off the system. So power supply is more likely...you might get a triple machine exception if you have a badly corrupted driver. Getting a driver that badly corrupted is somewhat difficult if there isn't an outright hardware failure.
People usually think of using too much power to only be power rails going to the motherboard. There is one other case I know of which is quite possible, and perhaps common. The USB ports define standards of how much current the USB peripherals are allowed to use. USB2 has a lower maximum current than USB3. If your USB ports are consuming too much power, then a few seconds after powering on it is likely to simply turn the system back off. Disconnect your USB devices and see if it still has the issue during a cold start. Plug the keyboard and mouse in only after it starts, one at a time.
I did find one odd culprit like this in the past. Some USB3 connectors are backwards-compatible with older USB2 ports. In theory they just throttle back to USB2 speeds when in a USB2 port. One of my devices forgot to also consume less power...it tried to consume USB3 standards power from a USB2 port. This caused a shutdown similar to yours. Moving the cable from the USB2 port to a USB3 port solved this.
Too many USB devices can also cause issues. An externally powered USB HUB will get around this.