Attached quick patch which I applied to handle nvme device correctly.
With this patch, tc-install.sh can handle nvme0n1 as target device (not as partition) correctly:
Writing zero's to beginning of /dev/nvme0n1 <----------------- good
Partitioning /dev/nvme0n1 <----------------- good
Formatting /dev/nvme0n1p1 <----------------- good
mke2fs 1.45.4 (23-Sep-2019)
1+0 records in
1+0 records out
440 bytes (440B) copied, 0.001982 seconds, 216.8KB/s
UUID="ec8341c0-55d7-4045-957e-09eaaf68f4fb"
Applying extlinux.
/mnt/drive/tce/boot/extlinux is device /dev/nvme0n1p1
Setting up corepure64 image on /mnt/nvme0n1p1
Setting up menu for Tiny Core
Remove Active Flag on /dev/nvme0n1p1
Toggle Active Flag on nvme0n1p1
Installation has completed
Press Enter key to continue.
... this correctly create nvme0n1p1 partition,
tc@box:~$ sudo fdisk /dev/nvme0n1
Command (m for help): p
Disk /dev/nvme0n1: 119 GB, 128035676160 bytes, 250069680 sectors
122104 cylinders, 64 heads, 32 sectors/track
Units: sectors of 1 * 512 = 512 bytes
Device Boot StartCHS EndCHS StartLBA EndLBA Sectors Size Id Type
/dev/nvme0n1p1 * 0,1,1 1023,63,32 32 250069679 250069648 119G 83 Linux
and confirmed installed TinyCore can boot up properly.