Someone someday should make a list of the reasons Windows would put its EFI on a separate drive. If Windows saw an EFI already existed elsewhere, it would want to use that. It doesn't like more than one in the system. That situation exists when one installs
to a new drive while leaving the current installation still plugged in. But the install likely would end up in a dual-boot. That wasn't true in your first install, was it?
And I believe, if Windows can't find unallocated space for an EFI on the drive to which it is being installed, it will look elsewhere for unallocated space. That situation is realized when one creates a single partition encompassing the full drive & installs
into it. I think normally EFI would be omitted & C: would get the boot files & become the boot drive. But, I'm guessing, if it sees unallocated space on another drive, it would put the EFI there instead. You said, "I didn't make the partition first".
Are you sure the NVMe hadn't come already partitioned - i.e., the line you clicked for the install said "unallocated space"?
Anyway, here is that computer's site...
https://www.asus.com/us/Motherboards/ROG-STRIX-Z390-E-GAMING/HelpDesk_Download/
ROG STRIX Z390-E GAMING
The specifications page shows it to be ready for SSD & to have sockets suitable for NVMe...
1 x M.2 Socket 3, with M key, type 2242/2260/2280 storage devices support (both SATA & PCIE mode)*^2^
1 x M.2 Socket 3, with M key, type 2242/2260/2280/22110 storage devices support (PCIE 3.0 x 4 mode)
But it may be able to see NVMe & still be incapable to boot from it. I saw one article deep down on the FAQs page that mentions NVMe, but doesn't say whether it can be booted. And I read each of the little blurbs for all the BIOS updates. Here is the latest
one...

It doesn't mention NVMe - none of them did. But I would take it, if your version (shown in
MSInfo32) is less than 1005. That's a good date & a great computer - I think ASUS would want to have its BIOS be NVMe boot capable having sockets for it. Here is how...
https://www.asus.com/us/support/FAQ/1012815
[Motherboard] ASUS EZ Flash 3 - Introduction
After that, I would redo the clean install. Things look too wrecked to try to fix that install any other way. I guess - maybe - unplug all the other drives. Maybe Windows is purposely putting EFI onto a separate drive because it doesn't check, but assumes
BIOS wouldn't boot it otherwise. Then...
Ensure BIOS is set for UEFI mode. Boot to the Installation media with the UEFI boot option. Click "Install Now", then "Custom Install". At the "where do you want to install Windows" screen - delete both/all partitions on Disk 3 so that only unallocated
space is left. Then select the unallocated space, & click next. This way should automatically create 4 partitions: Recovery, EFI, MSR, & Windows.
If that won't boot or create all 4 partitions, then plug back in the other drives, redo the install, & let it put the partitions where it will.
After the clean install, go back to the site & update all the drivers that need it.