Does 刚开始工作的时候... mean "when starting work" (each day) or "when entering the workforce"?
刚开始工作的时候，什么最重要？


I'd interpret it as when entering the workforce, which  is the second meaning you listed. 

When someone says 刚开始工作的时候, I'd assume he meant when entering the workforce.  If they try to convey when starting work each workday, I'd expect something like: 每天早上开始工作的时候; 每天开始工作的时候; 每天开始工作时; 每天工作开始时. 

One could bend that rule/convention sometimes, but it's not hard to figure out what they really mean in a given context anyway.