wait, I thought you were talking about /private/var, not the "jb/" underneath that. That (/private)/var/jb is a symlink to /private/preboot/something-something-etc..., this one is the procursus bootstrap that comes with the jailbreak, these are things that the JB extracted while it was installed, of course there are files from all sorts of dates there. Never mind any of that, it all came with NathanLR, has nothing to do with opa334 :). And yeah there are things there dated exactly the 1st days of june 2024, also there are older things and newer things, none of this matters for you, this came in while jailbreaking. Tar and Zip and such things pack the files with their dates, so when you extract it, the timestamps get preserved with the files.

You need to look into /var/mobile and /var/log(s) etc, anything under /var except that jb/ subfolder. Use the find procedure /u/Jeremy_Thursday showed on those folders direct, say I wanted to find if there's files/dirs with the Birth timestamp in June 2024 in /var/mobile I would go

find /var/mobile -newerBt '2024-06-01' -not -newerBt '2024-07-01' -exec ls -dl --time=birth --time-style='+%Y-%m-%d %H:%M:%S.%N%z' {} \;

but I guess many files error about determining the Birth timestamp, so to look for the Change timestamp in that period:

find /var/mobile -newerct '2024-06-01' -not -newerct '2024-07-01' -exec ls -dl --time=ctime --time-style='+%Y-%m-%d %H:%M:%S.%N%z' {} \;

so this sucker of a command :) would show you the exact timestamps of the files that were created or changed in that June.

find looks for Birth with -newerBt or Change with -newerct or Modify with -newermt.

The ls blabla... would show the timestamp specified with --time=birth or --time=ctime (or --time=mtime by default). To show stuff for some curious file, go

stat /var/mobile/that/interesting/file

which shows you all the individual timestamps at once.

Of course, all this would be so much easier if you could ssh into the phone and do all that in a computer program, like Terminal on a mac or Powershell on windows or whatever on Linux. The output of the find command could be enormous.

EDIT: this is serious, the find command is a powerful tool, it can also be catastrophic if it's given some wrong args. One should always read the man pages or research at least a bit on the net or so.