My best guess is that Google is “behind” OpenAI because Google is concerned that GPTs could negatively impact their core search business. OpenAI does not have that concern; so OpenAI is the “disrupter” and it remains to be seen what Google will do.
It’s like a country who has a fortune invested in new 5G mobile backbone, and the after they have spent a fortune on 5G, 6G comes out and blows away 5G. However, a country which may not have invested heavily in 5G can leap frog to 6G; but then they will face the 7G problem later on.
So Google, with a strong hold on search, will naturally be concerned with any new potentially disruptive technology which will impact their search business.
This means it is too early to predict how Google will play ball in GPT; but Google is certainly very capability of producing a “great GPT offering”; but the bit questions are “will they make it public?” “will it remain open source?” “how much will it cost?” etc.