but in Crypto Currency, how on earth can you prove that you had a wallet, and how much coins that wallet had?
even if the Blockchain has the history of that wallet address, how can you prove that wallet is yours??!

Well corporations that handle sizable amounts of data typically back up everything regularly as part of a standard operating procedure. If a hack steals everything
and erases everything to the point of zero recovery, then the hacked company is either completely and utterly incompetent,
or the "hack" was internal. I would find the latter scenario infinitely more likely in this case. Regulators are going to be way up in their ass either way.
That being said, I don't think it's going to be a problem of proving how much belonged to you as much as them paying out the said amount.