Yes! You can sign up for Premium at any time and return to earn your Premium prize that same day. You will only get the Premium prize for the day you signed up, but for as long as you're a Premium member, you'll be able to get daily Premium prizes on future days of the event! There's no way to go back in time and get Premium prizes for days that have already passed.
Once you've signed up, return to the page and donate another item to get your Premium prize for the day. If you have already hit your Daily Point Limit, go to the Donation section of the Hub page and click on the "Claim Prize" button. You'll get a pop-up revealing your Premium prize.