Yes, that "where do you want to install" picture is showing a completely empty disk. And I like seeing the word "unallocated" instead of "free" there. It means Windows is dealing with a GPT instead of MBR style disk. That's a solid indicator BIOS is set in UEFI mode & the installation media was booted correctly.
But all you needed to do there was to select the unallocated space, then click "Next". Setup would then create all the partitions necessary & give the Windows partition maximum space. But it does look like what you did resulted in the same outcome. Still - I would want to try it without clicking "New" next time. It is "foolproof" that way, Greg Carmack says in that URL I cited.
I did a BING of "initialization is unsuccessful for windows 10 setup" & came up with nothing concrete. But it sounds like a file necessary to boot is bad, maybe something on the EFI system partition. But that must be brand new since this is a clean install.
Might be a good idea to make a new Win 10 Installation media, the download might have been faulty.