The google search console is used to get statistics about the performance of your website in google searchs.
One of the methods of verifying that a website you add is really yours is by using “Google Analytics”.
My conclusion is that if you manage to insert your google analytics script to some website then you might be able to verify that website as your own and add it to your google search console.
Note: I did not test this theory and it is just something that I thought of now when verifying a website I own using google analytics.
However: another method of verifying ownership of a website is by inserting an HTML meta tag to the website home page or uploading a special html page to the website. So a strong stored xss or file upload can also be used to bypass the website ownership verification.