I'm familiar with tools such as ps and top, but to my knowledge, they don't catch all new processes. top has a log mode, but if the process is short-lived enough (e.g. echo 'Hello, World!', then the process won't be logged.
This being said, is there any way to just list all newly-created processes as they are created?
It sounds like what you want is "process accounting".
If you are using Linux, then there is a package called psacct that you can install and start.