The action should be brought as soon as possible or at least notification should be given to all parties who are potential defendants as soon as possible.
You should contact an attorney as soon as possible after such a fall or after something has fallen. The actual legal case can then be instituted later, though never more than three years after the date of your accident. However, it’s up to the individual attorney to make that kind of strategic decision. If you’re hurt, you should contact an attorney immediately.