Good question... I know that Google Translate began as a pretty bad outsourced translator (SYSTRAN) because I had a lot of trouble figuring out when Translate first came out for my Google survival analysis, and it began being upgraded and expanded almost constantly from ~2002 onwards. The 2007 switch was supposedly from the company SYSTRAN to an internal system, but what does that mean? SYSTRAN is a proprietary company which could be using anything it wants internally, and admits it's a hybrid system. The 2006 beta just calls it statistics and machine learning, with no details about what this means. Google Scholar's no help here either - hits are swamped by research papers mentioning Translate, and a few more recent hits about the neural networks used in various recent Google mobile-oriented services like speech or image recognition.

So... I have no idea. Highly unlikely to predate their internal translator in 2006, anyway, but could be your 2012 date.