No Google does not own the internet even though it seems like it.
The internet is not really owned by one company because it takes several companies and data centers etc to make the internet work.
So basically the internet is owned by just about everyone because without them we wouldn't have the internet.
Such as the data center to host all the websites are owned by different companies.
Google owns a lot of data centers but there are a lot of websites hosted on other servers in other data centers.
Not every website you visit through google search is hosted through google and is hosted through many different web hosting companies.