I think the first filesystems had flat layout (no directories), but also had different file types for a library, an executable, a plaintext file. Then there were filesystems where directories could only list files, not other directories.

The original Macintosh filesystem was flat, and according to WP, used for about two years around the mid-1980s. I don't think I've ever used it, personally.

https://en.wikipedia.org/wiki/Macintosh_File_System

MFS is called a flat file system because it does not support a hierarchy of directories.

They switched to a new, hierarchical filesystem, HFS, pretty soon.

I thought that Apple ProDOS's file system -- late 1970s to early 1980s -- was also flat, from memory. It looks like it was at one point, though they added hierarchical support to it later:

https://en.wikipedia.org/wiki/Apple_ProDOS

ProDOS adds a standard method of accessing ROM-based drivers on expansion cards for disk devices, expands the maximum volume size from about 400 kilobytes to 32 megabytes, introduces support for hierarchical subdirectories (a vital feature for organizing a hard disk's storage space), and supports RAM disks on machines with 128 KB or more of memory.

Looks like FAT, used by MS-DOS, early 1980s, also started out flat-file, then added hierarchical support:

https://en.wikipedia.org/wiki/File_Allocation_Table

The BIOS Parameter Block (BPB) was introduced with PC DOS 2.0 as well, and this version also added read-only, archive, volume label, and directory attribute bits for hierarchical sub-directories.[24]