I can prove it via knowledge about when it was created(15 min frame), when it was accessed last time, when it was abandoned, what IP address was used, and then the password. If required I can probably find associated address on blockchain. I think that should be enough.
I guess that's enough, they might say that you're the actual owner of the wallet base on the details you have and base on their record. But still I doubt they can help you to fully access your wallet's fund again since they stated that they can't access anyone's wallet and even they didn't know their user's password (not sure though since they only said that way), though they have some ways to recover your wallet but only using the email to seed, and unfortunately you don't have it...
Well, I just need them too look up wallet id(same as login basically) based on information I provide them, that's all! I have everything else required to access the funds. They surely can do this(and I hope they will), and even their authomatical support answer suggests that.
If you have misplaced or lost your wallet identifier, please submit the email address associated with your wallet to the following link in order to receive a reminder,
https://login.blockchain.com/#/reminderBear in mind that if the email address was misspelled during wallet creation, or if you do not have access to the email address associated with the wallet, then this method will not help resolve your issue. However, our support team may still be able to locate the wallet ID for you. In order to locate a wallet identifier we require both the email address and the IP address used to create the wallet.
(cut non related out)
If none of the above methods have helped you locate the correct wallet identifier, then, as a last resort, our support staff may be able to track down a wallet identifier if provided with both the password and the date this wallet was created. Please limit potential creation dates to a one week window. We are unable to search for a wallet based on bitcoin addresses used or transactions made within the wallet.
There sure wasn't that many wallets(probably only one) created in 15 min frame 4 years ago, with no mail, specific IP and afterwards access time.