file age

How can I count the age of the file (e.g. in minutes)?

It's not clear from your query what are you actually need.
If you simply want to find out was this file was modified (or created) in the
last 'n' minutes, you can use 'find' command:

find . -mmin 5 -name 'infile'

I spent more time than I should have looking for a solution to this and didn't find one.

If you do `ls -l` in a directory, you get a list of "last modified" dates, so you could perform some math in a script to tell the number of minutes since the last time the file was modified.

But as far as I can tell, Unix simply does not keep track of the date a file was created.

Unix does not track file creation dates...at least not so far as I know.

As normal dating use minutes, hours, days - that are reset after they reach some low maximum values, and as different months may have different number of days, it may be tricky to implement time difference calculation using normal dating. Instead a solution using the total number of seconds since a fixed date is simple and straight-forward. The Unix epoch time starts at new years moment 1970 and counts the number of seconds since then. The age of a file in seconds is then
EpochTime(now) - EpochTime(file). The shell script below uses modification time from date +%s -r referring to a file:

#Present time in Epoch Time measured
nowEpTime=`date +%s`
#Modification time of file in Epoch Time units.
filemodifEpTime=`date +%s -r $fil`
#Age in seconds
filageSeconds=$(($nowEpTime-$filemodifEpTime))
#In minutes
tdiff=$(($filageSeconds/60))
echo $tdiff