According to the department of labor and industry one can file for unemployment in the first week in which one works no hours or less than one's standard workweek. Since I knew I'd miss two days of work (Friday and Saturday), the week I got fired was the first week in which I worked less than 40 hours. So I was eligible to file. My first bi-weekly claim myst be filed the week of 6/6.

I wanted to get in in particularly early because I expect the agency to fight it.