I'm new in here and I know this thread is five years old but no-one seems to have put a proper answer on here.
The production date on a vgn-sz2m/b is etched on the top of the deck/palmrest panel. It's at the right hand side, underneath the cursor keys of the keyboard.
You won't see it until you lift the keyboard but that's not so hard, it doesn't even need to be disconnected.
On the back of the notebook, next to the docking socket cover, there is one screw recessed into the case. This is the keyboard security screw. Remove that screw then turn your notebook back over and with a thin probe push back and release the two locking tabs at the top of the keyboard, between the F1 & F2 keys and above the Insert/Pause key.
The keyboard should pop up from the top. Carefully lift it up, only about an inch or so, and slide the keyboard forward (towards the screen) and out of the locating tabs at the bottom, just far enough to spot the manufacture date on the deck panel.
Write it down, carefully locate the keyboard tabs again and lower the keyboard back into place. If you gently press down near the latches with your thumb you should hear the latches click into place.
Turn over the notebook and replace the security screw and you're back where you started but with your curiousity satisfied!
Usually, it's on the serial number itself. see if there's a 12 or 11 combination. I would call support for a quick answer too. They get that question a lot. It will only take a few minutes of your time.
no reason really except I was looking for info for myself and stumbled across what looked like something I could expand on. I know its not the only way of finding out and it relies on never having changed the deck panel but if it helps someone it can't do any harm.