Thank you @Rory !
I am not sure, that this post is related to my problem, though. It's not that I can't boot Zorin from the USB. That works without any problem. I can run it live and access the partitioning options and everything. It is just during the installation of Zorin that after the step "install alongside Windows" it won't recognize the NVMe drive.
Others have posted having this same trouble. Rory did, as well:
As I recall, many were using nVME, too.
I have nvme, and never had issues with Linux
Oh sorry! Now I understand it has to do with detecting the Windows 10 installation and not just the hard drive? Alright, then I will give it one more chance following all the steps. Thanks for clarifying!
Reading Rory's post, it looks like he covered both issues in one post.
Yes, I could easily install Zorin on the NVMe, but I am having issues with the dual boot install. So it's kind of a Windows issue 
Yes, I had lot of issues with dual boot..
And fix is only one..SWITCH TO LINUX 
timothys_monster, this was also a similar case for me, though my drive is SSD. The thing is, I could install Zorin from the Balena etcher flashed USB but only if I enabled Legacy ROM option in the BIOS, even though it still boots using UEFI mode it allows Legacy ROM to work. When the Zorin install routine ran it simply refused to recognise my EFI drive and as such didn't recognise my Win10 installation.
The trouble was the Balena etcher flashed USB will boot both UEFI and Legacy, so it was misleading me.
After talking with Aravisian I tried Rufus etcher and couldn't even boot no matter whether trying UEFI/Legacy ROM disabled or UEFI/Legacy ROM enabled.
It was then only when the Zorin chaps came up with a fix that Aravisian potsed that I realised that grubx64.efi was not present on the Rufus flashed USB. However, it was present on the Balena flashed USB
So then when I turned off Legacy ROM in the BIOS and used the fix, because the Zorin boot option was not automatically recognised and had to be added in to the BIOS boot option, lo and behold the Zorin boot option appeared at boot time, the install ran and more importantly it did recognise my efi partition and did recognise the Win 10 partition so that I could select 'Install Alongside Windows' and dual boot my system.
EDIT: I should add that the key things for me were this:
Thanks everyone for your continuous support! (Which I haven't got from the Zorin team, although I paid for the support.)
Nothing can make the drive show up in the "install alongside Windows" option. I even tried another USB drive. Legacy on or off, choosing the grub file manually or starting the drive directly...
And I couldn't partition the drive manually. When I chose the free FAT32 partition it wouldn't be accepted (no root or something was the error)
I will now install Zorin on the SSD (SATA) that the installer shows me.
This usually happens when the mount point was not set. Did you set Mount Point to /
at the prompt? It is easy to miss.
Oh... I just left it untouched. But I guess I should have specified /
That might have been the problem... Now the installer is busy trying to partition my other drive 
It was. 
(cough)
Ima smack you upside the head.
This is why I didn't want to partition manually, hahaha! I knew I wouldn't be able to... Thanks for all your patience
Believe in yourself.
If I can do it, you definitely can.
I say this not because you are especially capable. But because I am especially dumb.