Side note: I didn't know Google had their own TLD. Is this new? Seems weird that an organization has that ability to do that.
Edit: s/can/could (thanks to child commenter).
And when you say “super involved”, keep in mind that part of the required process is to travel back in time to before April 2012, because “The application window for the first application round closed in April 2012. Comprehensive reviews of the program are currently underway to assess its performance in meeting intended objectives. These reviews will inform ongoing discussions with the ICANN community to determine when a second round will take place.” [0]
blog.google is used pretty often.
Anyone could during the one-time “new gTLD” scramble, but applications closed for that years ago; no decision on any subsequent round has yet been made, because the review of that first round has not yet been completed.
So, other than establishing a new country and getting a new ccTLD, there's no way to get a new TLD right now.
No, ICANN years ago allowed that for a limited time, and is currently reviewing the results of that to decide if, when, and how to do so again.
It might make sense by the logic of domain names, but it doesn't by the logic of return on the investment of scarce resources. cern.org or cern.ch or cern.anything would meet all functional needs just as well and for much less.