The modern notion of package-manager-with-builtin-download-and-uprades only came in the mid-to-late 90s, when internet bandwidth grew enough to make that feasible.
The first one of these might've been FreeBSD ports.
I did find VC history where the first thing to track software seemed to be SCCC on UNIX:
https://en.wikipedia.org/wiki/Source_Code_Control_System
The rest, from CVS to mainframe stuff to Apollo Aegis's, all showed up around mid-1980's in similar time frame per Wikipedia descriptions. pkg seems strong contender for first, package manager if even version control of source didn't hit others until after its creation.
So if we look at methods of tape distribution, even the very first edition of Unix in ~1971 had tap (an early ancestor of tar) [1] which saved & restored filenames, mtimes, modes, and owner info. You could argue that a tp/tar archive is a primitive packaging system.
[1] http://man.cat-v.org/unix-1st/1/tap
The other instance I can think of is the shar format [2] that was used to distribute software over Usenet from the early 1980s. Shar was basically a fancy text file that you piped through a shell (yeah, I know). Because binary compatibility was rare, most shar files resulted in a directory of source code, which you'd then compile -- basically, like a 'modern' tarball.
I'd definitely count that as an early packaging system if it had all that metadata with it. So, that pushes it back to 1971 unless a non-UNIX machine had an equivalent before that. Likely a business mainframe or academic machine.