BSOD on startup, sometimes seemingly at random. Brand new machine.

Hello Lou and welcome to the forum.
You may want to enable XMP mode for your memory using your system's BIOS utility and see if that helps the issue at all.
Failing that, Give memtest a try:

IF you start getting errors stop the test, remove one stick of RAM and start again.

 

It has been a week and without going back and looking though your dump file(s), I feel relatively safe in saying that yes a BIOS update might be helpful.

And I'm pretty comfortable admitting that the only thing I'm sure of, is that I'm not sure of anything when it comes to BSODs.
I would suggest that after testing your memory as suggested above, if it tests good then I would move next to your hard disk
Use the native Check Disk utility
chkdsk C: /R
and follow that up by using the vendor specific hard disk diagnostic utility provided by your hard drive manufacturer a list of some of which can be found here Hard Drive Diagnostic Procedure
If the machine is crashing consistently before even loading the OS, then that would suggest a likely hardware issue, so double check all your connections (power and interface cables), double check all addin modules (cards, memory, even CPU) for proper seating and of course make sure that whatever power supply you have chosen, that it is up to the task of supporting the power demands of all your components.