Cobalt is correct. unlike Chevy, it's not stamped on the deck.
It IS possible, the partial VIN is stanmped vertically along the side of the timing cover, as previously suggested. Usually, it' covered with "yuck", but when cleaned up, readable. There may also be a "SR" stamped alongside the cover. That's a "Service Replacement" (warranty block) and many were "restamped" by dealers early on. I recall putting the codes on a 455SD under instruction from Pontiac, when they replaced one under warranty.
Thank you for refering to the transmission correctly. Many simply call it "TH400", because it is essentially the same except the case. Pontiac called it "M-40".
There's something really cool here, many are missing. You have a '68 GTO!!! (lucky ******!).... The "YS" indicates a 350HP 400 /auto trans. Is the "His and Her's" shifter still there? Let us know when you want to get started on restoration or modernizing! A couple of these guys are real sharp on the Pontiac.