All ads displayed in the results have availabilities matching the dates you entered for your search, meaning you can start searching as soon as possible to put all the odds in your favor. If you don't enter a date, you will see which accommodations are available immediately. You will also see from which date the accommodations that are not available immediately will become available.
This being said, many tenants, especially those in student residence, have one month to give notice of their leave. Do check search results regularly, as new units become available over time.