The transition to using GPU accelerated algorithms at scale started happening pretty early in Google around 2009/2010 when they started doing stuff with voice and images.
This started with Google just buying a few big GPUs for their R&D and then suddenly appearing as a big customer for NVidia who up to then had no clue that they were going to be an AI company. The internal work on TPUs started around 2013. They deployed the first versions around 2015 and have been iterating on those since then. Interestingly, OpenAI was founded around the same time.
OpenAI has a moat as well in terms of brand recognition and diversified hardware supplier deals and funding. Nvidia is no longer the only game in town and Intel and AMD are in scope as well. Google's TPUs give them a short term advantage but hardware capabilities are becoming a commodity long term. OpenAI and Google need to demonstrate value to end users, not cost optimizations. This is about where the many billions on AI subscription spending is going to go. Google might be catching up, but OpenAI is the clear leader in terms of paid subscriptions.
Google has been chasing different products for the last fifteen years in terms of always trying to catch up with the latest and greatest in terms messaging, social networking, and now AI features. They are doing a lot of copycat products; not a lot of original ones. It's not a safe bet that this will go differently for them this time.