It wouldn't be anywhere near that simple:
* If there are security vulnerabilities in Mastodon and Google is hosting an instance then Google would be blamed, which means they would need to do a very thorough security review before hosting one.
* If they announced it and lots of people wanted to join it would probably have far more members than the biggest Mastodon instances do today, so they would want to make sure they had something that could scale horizontally. I don't think the current codebase can do that?
* There are various places where the current design of Mastodon doesn't match user expectations around privacy and control over their content. For example, if you delete something it looks to you like it's deleted but that delete may not fully propagate. By hosting a server Google would be taking responsibility for this, and would have people mad at them (likely with lawsuits) when it didn't do what they expected.
This isn't to say that Google would never get into the federated social network space, but it would be after building their own activity pub implementation.
(Disclosure: I used to work at Google)