macOS / APFS do
not fundamentally disallow dates before 1970 on the file system level at the very least:
Console Output: Select all
$ touch -d 1968-01-0100:00:00 a.txt
$ stat -x a.txt
...
Access: Mon Jan 1 00:00:00 1968
Modify: Mon Jan 1 00:00:00 1968
Change: Fri Aug 16 03:30:00 2024
Birth: Fri Aug 16 03:30:00 2024

But if you're using a Linux-based NAS that you access from macOS, then anything is possible. Depending on your software configuration, what you want may or may not be possible due to software compatibility issues.

Notably, macOS does have a dedicated
"file creation date" and
"last-modified date" fields. Linux does not, and so on Linux, setting one may also set the other and vice versa. That can be confusing. On top of that, if you're using a remote file system, then there's gonna be another layer of translation where things can go awry. That's probably where the
2262 dates are introduced, as signed integer negative time stamps are misinterpreted as unsigned integer positive time stamps at some point.
EDIT:

Adding to the confusion, even local
macOS / APFS may behave inconsistently when dates before 1970 are at play, i.e. setting
Last-Modified may or may not also set
Creation-Date implicitly depending on the dates at play:
Console Output: Select all
$ stat -x 2*
File: "2001 - A Space Odyssey (1968).mkv"
...
Modify: Tue Apr 2 00:00:00 1968
Birth: Tue Apr 2 00:00:00 1968
$ touch -d 1980-01-0100:00:00 2*
$ stat -x 2*
File: "2001 - A Space Odyssey (1968).mkv"
...
Modify: Tue Jan 1 00:00:00 1980
Birth: Tue Jan 1 00:00:00 1980
$ touch -d 1940-01-0100:00:00 2*
$ stat -x 2*
File: "2001 - A Space Odyssey (1968).mkv"
...
Modify: Mon Jan 1 00:00:00 1940
Birth: Tue Jan 1 00:00:00 1980