This is actually a decent question. I don’t believe there is a simple answer. Maybe cloning the drive before and after would glean some clues? Barring that, I think maybe using find would help? Something like this; proof of concept:
find ~ -type f -cmin -30 | more
That command specifically would use find to search for any item in your home directory (~) that is a file (-type f) that has been created in the last 30 minutes (-cmin -30). The output of find is piped to more for easy reading, but you could also send the results to a file for later review like this:
find ~ -type f -cmin -30 >> find_file.txt
Now of course this is far from perfect for a per application review of what has been installed. Not to mention that for the purposes outlined in the question, the directory path of ~ would have to be expanded to cover the whole drive with / like this:
find / -type f -cmin -30 >> find_file.txt
But at least this gives you something to start with. Perhaps do a scan like this before the software install and the after the software install, diff the documents and take it from there? Run this find command before you install software:
find / -type f -cmin -30 >> find_file_before.txt
Then run this find command after you install software:
find / -type f -cmin -30 >> find_file_after.txt
Then just diff those two files.
Of course you can experiment with changing the -cmin -30 to something smaller like -cmin -10 or even longer like -cmin -60 but that depends on your goals. And of course your life would be made easier by filtering out some caches/ephemeral files that just get created/trashed by the system in normal use. But then again, focusing on what exactly you would want to ignore from a find connected to a software install is up to you to explore and refine.