Prove means something differently here. You subpoena records and get every damn email, piece of paper, SMS, meeting transcript, etc. related to the computers. You get invoices from contractors who worked on it. You subpoena the people involved and establish exact timelines of what everyone did, and when.

If these records are incomplete, the judge decides against the police with prejudice.

If the records are complete and there isn’t indications they copied the data and performed analysis entirely off the books, then we say that we’ve proven analysis didn’t happen.

You can't, unless very specific measures were taken beforehand (which doesn't happen normally). You need to testify under oath that you did and the other side needs to hope that the punishment for lying under oath is worse for you than the consequences for them when it wasn't deleted.

Paper trail of where it could have ended up maybe? And I mostly mean that if the testifying human isn't impartial, he would require physical evidence to corroborate his testimony, despite the oath.

The reason being sufficient examples and even game-theoretic arguments (mind you, these are 'nerds', they can find someone well-versed in game theory if needed) show a lack of (expected) trustworthiness of a non-corroborated testimony of such a human.