Can you explain more about what you mean when you say the testing assignment is “time-driven”? Does this mean that you have a certain amount of time to execute the test and the test will pass or fail based on the time it took to execute?
Whether or not you automate will be dependent on many factors. Automation typically will speed up your test execution, but will take time to develop and maintain. There are also many different types of automation. Often people think of test automation as the User Interface testing using record and playback tools. However, there are of course ways to automate for performance testing, unit testing, or many other types of tests.
If your “time-driven test” is meant to test performance, then Id suggest performance test automation.