Let's just say that you want to prove that unauthorized access has happened to a GMail account. You know from where that would've occurred. Google's "Last Account Activity" shows currently active sessions but what if the suspected access happened a month or more ago? Does Google keep records about how the account has been used? If so, hwo would you go about getting them?
Through a lawyer.
Google will need to find the data, verify your identity, ensure that they're complying with any legal requirements, ensure they're only providing data for your account and not any other accounts that might have used the same IP addresses, etc. It'll probably pass through at least two or three people at a cost of hundreds of dollars in labor. Google aren't going to provide this information unless they have a legal requirement to do so.