You cannot use init. It is the wrong program for the job.
You need to un-learn the idea that init can be invoked as a normal command. The init programs where this is/was true are not the init program that you have. There are 4 init programs where one can invoke it as a normal command, and you are not using any of them. Rather, you are using BusyBox init,...
OK, I found the answer myself.
After removing the quiet kernel option it showed some errors about the SELinux contexts.
The problem was the selinux kernel module.
I started the system with selinux=0 kernel option in grub to prevent selinux from loading and it worked!
OK, I managed to install Pop!_OS 19.10 to the PC now, though it first did not want to do it (somehow Rufus does not flash the image properly, had to use Etcher).
NTFS-problem => just wipe the disk
Medium not found => change from USB3.0 to USB2.0
Mouse/Keyboard not responding after boot => enable IOMMU (might be Gigabyte-specific solution)
It sounds like there is a broken NTFS filesystem, or partition table on the SSD, which is causing the message about the unclean filesystem. You could try making a new partition table on the disk, and then making new partitions. The archwiki article on partitioning has a good intro to partition table types, disk partitioning and suggests some linux tools for ...