Hi,
Very likely! It strongly depends on how the events and the event data is stored. There is very likely a date field of some sort, where you can specify the event start and end dates?
Usually creating a date filter (it does not have to be visible) to exclude the events ending before the current date is the trick. For that however we need to know what the field name is. Do you use any plugin by any chance to store the events, like Events Calendar or similar?