Why don't we have a way in Linux to know when a particular file was created?

Linux DOES have a way!  

The various filesystems have what they have, no more no less - pondering why they are as they are isn't productive.  They don't track creation-time metadata properly, and that's that.  The GREAT news is that the design of a workable solution isn't complex at all.  It's pretty straightforward.

The inotify kernel subsystem has been part of Linux since 2005 but it's still relatively unknown.  You can use it to learn when new files are added to directories, among other things.

So, if you choose to solve this problem, you'll build a daemon to monitor new files as they're created, and put their create times into a dataset you can later query.

Start with logic which recurses over whatever directory trees you wish to track, creating "inotify watches" on each directory.

Use a loop which calls "select" across that large array of file descriptors, one-per-directory, and reads the inotify events from the individual fds as they happen.  IN_CREATE events are the ones you'll be looking for - those indicate new files were created.  

Capture the ctime of the file as soon as you have received the IN_CREATE event indicating it was created, and, viola, you have it's "cr_time".

Next.  Implement in whatever way you prefer a persistent associative array of filenames -> creation timestamps.  

You might also implement the inverse, mapping creation timestamps to the file or files which were created at that time, to whatever granularity you prefer.

You can then query the creation time for a given file quite straightforwardly, and if you've implemented the inverse as I mentioned, you can query which files were created between two timestamps as well.

If you named it "pfcmd", short for "Paul's File Creation Monitor Daemon", I wouldn't mind one bit.  :-)