How long a trip were you planning?
You can book the first two nights on a separate reservation and then check out and check back in on a package, to get free dining for the rest of your stay.
But you're definitely out of luck for the first two nights. Problems arise if you want
DDP for those first two nights at all - because unless you have an annual pass you'd have to book a separate package AND buy tickets with that package to get the DDP. That means you will be buying tickets with BOTH packages. That might actually negate whatever savings you could get out of free dining.
If you can get by without DDP for the first two nights, you can book your full length of stay tickets with the free dining package starting the 22nd, then pick them up separately from the package two days early. There's no way to start the dining two days early though...you can only do that with the tickets. See the Ticket FAQ on the Theme Parks board for information on how to do this. Apparently you have to go to Guest Services to get the tickets, you can't just pick them up at the resort.
The other option is to rent points from a DVC member for the first two nights, then have them add the dining plan for those nights (you'd be paying them for adding the plan, but you would not have to purchase any tickets to get it). But then you would most likely be changing resorts after the first two days.