Always an Insurmountable Catch 22

There are three ways to address this.

1. Bring your iMac Pro 2017-2021 (along with any other devices you plan to migrate from) to an Apple Store and ask for help. It’s a $5,000+ model after all, and you deserve it. From your post it seems there are a lot topics that need help for the setup.
2. Use Internet Recovery to reset and reinstall the iMac Pro. Apple guideline here Use macOS Recovery on an Intel-based Mac - Apple Support (CA). However this won’t guarantee that you will get the 10.13 in the end, and you might get a much higher OS version instead. ONLY restart the iMac Pro by pressing Option-Shift-Command-R. This will factory reset you machine to 10.13.2 if this is the original OS shipped with your iMac Pro. Some iMac Pro shipped later may have other updated versions from factory.
3. Fresh install 10.13 via bootable USB installer. Apple guidelines here How to download and install macOS - Apple Support and here Create a bootable installer for macOS - Apple Support. This link also have a step by step guide of installing the OS that I won’t repeat here.

There is no need to have access to SSU for it to work so no Catch 22 there. However it’s better to download and make the installer in a working Mac. It’s possible to do so in Linux or Windows though. Another potential Catch 22 eliminated.

Note: While installing the OS, using disk utility first is desirable to properly format/erase the disk. You might need to choose ‘View’ to show the Disk (not Volumes or containers) so that you can erase the entire disk and all partitions.

Make sure to use GUID Partition Table and APFS format for your iMac Pro. They are optimized for SSD.

One More Thing: 10.13 High Sierra is a good OS but most recent OS versions are better for your iMac Pro in many many ways. If you absolutely need some old apps in 32 bits, at least you can update to 10.14 Mojave which has a few good new features. I hate to mention it as this is a complex subject and also depends on specific use case. And eventually it will leads to square one.

Hope the above helps.

1) Shut off the iMac.

2) Plug in the external startup disk(s).

3) Startup holding the Alt (option) and choose Recovery or one of the bootable disks.

4) If nothing shows up in the Startup Manager, then you do not have any viable bootable disks.

5) If the iMac shuts down, does not startup in Recovery mode or from one of the bootable disks, then I would suspect it has a hardware issue that requires service.

I've been creating bootable external media for the last several years. I did have to learn how to change security to allow external booting on T2 chip machines but that was a a no-brainer.

After that I used Carbon Copy Cloner for a while to create bootable and then switched to SuperDuper! about a year ago. SD! has been perfect making bootable media. And the basic app was free. Only when I wanted to schedule cloning the differences (updating the original) did I need to buy the app. But then I believe in paying my way so the cost was just that of being a computer user.

We own: two 2020 27" Intel iMacs, one 2015 21.5" iMac, One 2016 13" MBP no touch and one 2020 13" MBP with touch. All have been to this day (actually yesterday) perfect with respect to bootable media (actually tested on them all) and by using an external SSD, the performance hit is hardly noticeable for what we do..

The external SSDs are Samsung T7 500 GB. They have performed flawlessly from the very beginning.

Changing the boot drive is incredibly simple: Option key at startup or select the bootable drive in System Preferences/Settings. The change "sticks" until I reset it.